Prove that

(1 + cot A + tan A) (sin A - cos A) = sin A tan A - cot A cos A

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

tan A = [tex]\frac{sinA}{cosA}[/tex] , cot A = [tex]\frac{cosA}{sinA}[/tex]

Consider the left side

(1 + cotA + tanA)(sinA - cosA)

each term in the second factor is multiplied by each term in the first factor.

1(sinA - cosA) + cotA(sinA - cosA) + tanA(sinA - cosA)

= sinA - cosA + cosA - [tex]\frac{cos^2A}{sinA}[/tex] + [tex]\frac{sin^2A}{cosA}[/tex] - sinA ( collect like terms )

= [tex]\frac{sin^2A}{cosA}[/tex] - [tex]\frac{cos^2A}{sinA}[/tex]

= ( sinA × [tex]\frac{sinA}{cosA}[/tex] ) - ([tex]\frac{cosA}{sinA}[/tex] × cosA )

= sinAtanA - cotAcosA

= right side ⇒ proven


Related Questions

Using this figure A’ is the______Of A.

Answers

Answer:

Reflection

Step-by-step explanation:

Figure A' is the reflection of A as it is reflected from A'

Which graph shows the axis of symmetry for the function f(x) = (x – 2)2 + 1?

Answers

Answer:

B - The correct answer is graph B

Step-by-step explanation:

Answer:

the correct choice is graph B. (see attachment below)

A plumber charges $70 per hour plus $40 for the call. What does he charge for 4 hours of work? Use x to represent the hours of work.

Answers

Answer:

Step-by-step explanation:

70x4 is 280 plus 40 is 320.

Answer:

$320

Step-by-step explanation:

(4 x $70) + $40 is the equation

$280 + $40 = $320

$320

I hate math bro please help me ill mark u brainliest

Answers

Please mark me brainless :)

One ounce of cheddar cheese contains 9 grams of fat. Six of the grams of fat are saturated fats. Find the ratio of saturated fats to total fat in an ounce of cheese.

Group of answer choices

6:9

2:3

3:2

9:6

Answers

Answer: 6:9

Just divide  saturatedfats/TotalFats=6/9

Step-by-step explanation:

Which is equivalent to 3 square root of 8 1/4 x

Answers

Answer:

3

33

x

2

Step-by-step explanation:

Simplify

(Something is wrong with my keyboard hopefully you can put this together I'm sorry)

35 because quien u as the 8 and the 3 it gives you 35

Simplify
(2 Points)
2a xa x 3a + b x 45

Answers

Answer:

[tex]6a^3+45b[/tex]

Step-by-step explanation:

[tex]2a\times a\times 3a+b\times 45[/tex]

[tex]2a\times 1a\times 3a+b\times 45[/tex]

[tex]2\times 1\times 3 \times a \times a \times a+b\times 45[/tex]

[tex]6a^3+b \times45[/tex]

[tex]=6a^3+45b[/tex]

Answer:

6a^3 + 45b

Step-by-step explanation:

=2a × a × 3a + b × 45

=2a × 1a × 3a + b × 45

=2 × 1 × 3 × a × a × a + b × 45

=6a^3 + b × 45

= 6a^3 + 45b

Four lines extend from point K. The space between lines K J and K N is 58 degrees. The space between lines K N and K M is 61 degrees. The space between lines K M and K L is 61 degrees.

Which statement must be true about the diagram?
1. Point K is a midpoint of Line segment J L.
2. mAngleJKN = One-halfmAngleJKM
3. Ray KM is an angle bisector of AngleNKL.
4. JK = One-halfKL

Answers

Answer:

Ray KM is an angle bisector of AngleNKL

Step-by-step explanation:

Answer:

Ray KM is an angle bisector of AngleNKL

Step-by-step explanation:

brainlist???????????

Stefani took a science test. she answered 42 questions correctly. There were 50 questions on the test. What percent of the questions did she get right?

Answers

Answer:

She get 84% right

Step-by-step explanation:

42 x 2 = 84

50 x 2 = 100

Answer:

84%

this is the picture of how I solved it.

hope you understand.

can you please help me with functions

Answers

Option D is the right answer

(-1,4),(1,7),(2,10)

It is a function because input X values have its unique output y values.

hope it helps

Good luck on your assignment

Solve the equation 2x^2 – 3x – 5 =
10x to the nearest tenth.

Answers

Answer:

Step-by-step explanation:

a factor of 30 is chosen at random, what is the probability that the number has 2 digits?

Answers

Answer:

3/8

Step-by-step explanation:

Let's first start by figuring out all the factors of 30.

They are as follows: 1, 2, 3, 5, 6, 10, 15, 30

30 has 8 factors in total.

3 of the factors have 2 digits.

Probability is number of desired outcomes/number of total outcomes.

We have 3 desired outcomes and 8 total outcomes.

Therefore, the probability that the factor chosen at random will have 2 digits is 3/8.

pleaseeeeee right answer struggling

Answers

The right answer is of:

option C

please see the attached picture....

Hope it helps.....

Good luck on your assignment.....

5 Write the first five terms of the sequence with nth term.

a 4n
b 2n+1
c 3n -2
d 1/2n +1
e 20 -5n
f -2n +3​

Answers

Answer:

its a lot u'll see at the end

Step-by-step explanation:

a) 4n = 4,8,12,16,20

b) 2n+1= 3,5,7,9,11

c) 3n-2= 1,4,7,10,13

d) 1÷2n+1= [tex]\frac{3}{2}[/tex], [tex]\frac{5}{4} ,\frac{7}{6} ,\frac{9}{8} ,\frac{11}{10} ,[/tex]

e) 20-5n= 15,10,5,0,-5

f) -2n+3= 1,-1,-3,-5,-7

took me a while hope it is helpful

Identify whether the relationship between ∠a and ∠b in the image below is complementary, linear pair/supplementary, or vertical.

Answers

Answer:

see below

Step-by-step explanation:

Because there is the right angle symbol on the chart these angles are complementary meaning thety have a sum of 90°.

What is the product of 5.86 × 10–7 and 3.1 × 104 1. Write the expression: (5.86 × 10–7)(3.1 × 104) 2. Rearrange the expression: (5.86 × 3.1)(10–7 ∙ 104) 3. Multiply the coefficients: (18.166)(10–7 ∙ 104) 4. Apply the product of powers: 18.166 × 10-3 5. Write in scientific notation: 1.8166 × 10n What is the value of n in the scientific notation of the product? n =

Answers

The product of the given values in scientific notation would be = 1.8166× 10-2.

What is scientific notation?

Scientific notation is a method that is used in arithmetics to represent numbers and figures that are too large or too small and usually raised to power of 10.

The values that are given for multiplication is as follows;

5.86 × 10–7 × 3.1 × 104

First rearrange the expressions;

(5.86 × 3.1)(10–7 ×10⁴)

The multiple the coefficients;

(18.166)(10–7 ∙ 104)

The apply the product of power by addition of the powers;

18.166 × 10-3

The scientific notation representation of the product = 1.8166× 10-2

Learn more about scientific notation here:

https://brainly.com/question/27862246

#SPJ1

WILL GIVE BRAINLIEST What are the like terms in the algebraic expression? Negative a squared b + 6 a b minus 8 + 5 a squared b minus 6 a minus b Negative a squared b and negative 6 a Negative a squared b and 5 a squared b 6 a b and 5 a squared b 6 a b and negative 6 a

Answers

Answer: B

Negative a squared b and 5 a squared b

Step-by-step explanation:

Given that:

Negative a squared b + 6 a b minus 8 + 5 a squared b minus 6 a minus b. That is,

- a^2b + 6ab - 8 + 5a^b - 6a - b

Collecting the like term by rearranging the expression

5a^2b - a^2b + 6ab - 6a - b

The like terms in the expression above are

5a^2b - a^2b.

The correct option is B:

Negative a squared b and 5 a squared b or (-a^2b and 5a^b)

Answer:

B

Step-by-step explanation:

Negative a squared b and 5 a squared b

Step-by-step explanation:

Given that:

Negative a squared b + 6 a b minus 8 + 5 a squared b minus 6 a minus b. That is,

- a^2b + 6ab - 8 + 5a^b - 6a - b

Collecting the like term by rearranging the expression

5a^2b - a^2b + 6ab - 6a - b

The like terms in the expression above are

5a^2b - a^2b.

The correct option is B:

Negative a squared b and 5 a squared b or (-a^2b and 5a^b)

Write the recursive function for the following sequence. 0, 4, 8, 12,

Answers

The answer is +4
Explanation

The base of this solid crate has an area of 6 square meters. The height of the crate is 4 meters. What is the volume of the crate?

Answers

Answer: 24 m^3

Step-by-step explanation:

Given that you have a base with an area of 6 square meters, it has already calculated the product of length and width. In the Volume Formula Length x Width x Height, you're pretty much multiplying that given area by a height of 4, since you already have that length and width in the form of 6 square meters. The result you'll have is 24 Meters Cubed.

Which ordered pair is a solution of the equation? 5x+12y=60

(0,5)
2, 25/6
both
or neither

Answers

Answer:

both

Step-by-step explanation:

you can solve this problem with substitution:

5(0) + 12(5) = 60

0 + 60 = 60 is true, therefore the first ordered pair is a solution

the second ordered pair is:

2, 25/6

therefore:

5(2) + 12(25/6) = 60

10 + 50 = 60

10 + 50 = 60 is true, therefore the second ordered pair is also a solution.

in conclusion, both of the ordered pairs are solutions.

What is the domain of this function. (Could someone explain it too? I wanna be able to do it myself as well)

Answers

[tex]answer \\ = - 2 , 2 ,3 , 4 \\ explanation \\ let \: r \: be \: a \: relation \: from \: a \: to \: b. \: then \: \\ the \: set \: of \: first \: components \: or \: the \\ set \: of \: elements \: of \: a \: are \: called \\ domain \: and \: the \: set \: of \: second \\ components \: or \: the \: set \: of \: elements \\ of \: b \: are \: called \: the \: range. \\ hope \: it \: helps[/tex]

Which words or variables mean OUTPUT? Select all possible answers. help me out

a. domain

b .range

c .x

d .y

e. f(x)

Answers

B. Range
D. Y
E.f(x)
y is always the output, and range and f(x) mean the same thing along with Y
b.range

c. y

e. f(x)

Please help me (this is one questionn)

Answers

Answer:

Below.

Step-by-step explanation:

Reading off the graph:

y-intercept  = (0, 2.5)

x-intercept = (3.5, 0)

Last week, Jason ran 26.1 miles. He wants to run further this week. He plans to run 2.4 miles to the park, four times around the park, and 2.4 miles back from the park. To represent that inequality, he wrote: 2.4 + 4p + 2.4 ___ 26.1 Which inequality symbol should he use? Why?

Answers

Answer:

Greater than (>)

Step-by-step explanation:

Last week, Jason ran 26.1 miles.

He wants to run further this week.

Distance Run this week

2.4 miles to the park, Four times around the park= 4p (if distance around the park is p miles) 2.4 miles back from the park.

Total Distance this week =2.4+4p+2.4

Since his distance this week is going to be greater than the total distance covered last week (26.1 miles), we then have:

Total Distance covered this week > Total Distance Last week

[tex]2.4+4p+2.4>26.1[/tex]

Jason should use the greater than inequality sign.

Answer:

He should use the greater than symbol, >. He would not beat his distance if he only ran 26.1 miles, so the greater than or equal to symbol would not be correct.

Step-by-step explanation:

Jamie knows the lengths of 2 sides of a triangle are 8
and 12. Use the Triangle Inequality Theorem to determine
the possible values for the length of the third side of Jamie's
triangle.

Answers

[tex]answer \\ 4 < s < 20 \\ solution \\ 12 - 8 < s < 12 + 8 \\ = 4 < s < 20 \\ hope \: it \: helps[/tex]

Find a value for Ф in radians between 2π² if sin(Ф) = -1/2 and cos(Ф) = √3/2 (Unit Circle)

Answers

Answer:

This is the angle in the angle in the fourth quadrant that verifies the given conditions:

[tex]\phi =\frac{11\, \pi}{6} \\[/tex]

Step-by-step explanation:

Notice that in the unit circle, if sin of the angle is negative, and cos of the same angle is positive, we are in the fourth quadrant.

Also, the angle that renders

[tex]sin(\phi)=-\frac{1}{2}[/tex]

in the fourth quadrant, is [tex]\phi =\frac{11\, \pi}{6} \\[/tex]

for such angle, also :

[tex]cos(11 \pi/6)=\frac{\sqrt{3}}2}[/tex]

which verifies the second condition.

Which ratios is equivalent to 12 over 2 ?

Answers

Answer: 12:2, 6:1, 24:4

Step-by-step explanation:

2⁄5 + 3⁄7 + 5⁄6 = is what?

Answers

Answer:1.661905 or 349/210 Or 1 139/210

Step-by-step explanation:

2⁄5 + 3⁄7 + 5⁄6

29/35+5/6

349/210

1 Point
Which of the following is a disadvantage of speaking your ideas rather than
writing them?
O
A. You are not able to express your emotions as easily.
B. You will not be able to correct spelling errors.
C. You cannot be casual and spontaneous when speaking,
D. You cannot plan ahead and organize your thoughts.
SUBMIT

Answers

Answer:

D.

Step-by-step explanation:

You cannot plan your thoughts if you are just thinking out loud.

The answer is D

You cannot plan ahead and organize your thoughts.

Lakesha is taking three of her friends to see the latest movie. Each ticket is $5.50, and she is paying for all four tickets. How much money does Lakesha need to bring to pay for all of the tickets? A. $16.50 B. $22.00 C. $49.50 D. $55.00

Answers

Answer: $22

Step-by-step explanation:

$5.50 * 4 = 22

Answer:

B. $22.00

Step-by-step explanation:

The expression you need to set up is 5.5 times 4, since she needs to pay 4 tickets and each is $5.50. After you multiply, you should get 22, which is the answer.

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