if a + b + c is equals to 270 then prove that sin a cos b sin c + cos a sin b sin c + sin a sin b cos c = cos a cos b cos c​

Answers

Answer 1

Answer:

[tex]Solution,\\a +b+c=270\\or, a +b = 270-c\\[/tex]

[tex]cos(a+b) = cos(270-c)~~~~~~~~~and~~~~~~~~~sin(a+b)=sin(270-c)\\or, cos(a+b) = -sinc,~sin(a+b) = -cosc\\Now,\\L.H.S. = sina.cosb.sinc +cosa.sinb.sinc + sina.sinb.cosc\\~~~~~~~~~~= sinc (sina.cosb+cosa.sinb)+sina.sinb.cosc\\~~~~~~~~~~=sinc[sin(a+b)]+sina.sinb.cosc\\~~~~~~~~~~=sinc.-cosc+sina.sinb.cosc\\~~~~~~~~~~=cosc(sina.sinb-sinc)\\~~~~~~~~~~=cosc[sina.sinb+cos(a+b)]\\~~~~~~~~~~=cosc[sina.sinb+cosa.cosb-sina.sinb]\\~~~~~~~~~~=cosc.cosa.cosb\\~~~~~~~~~~=cosa.cosb.cosc \\[/tex]

Hope I helped you!


Related Questions

Luisa sells stuffed animals. She sells a stuffed elephant for $34.90, and the sales tax is 9% of the sale price. About how much is the sales tax on the elephant?
$3.15
$4.90
$0.32
$4.95

Answers

Answer:

OH DADDY FASTER

Step-by-step explanation:

OY PAPI MAS RAPIDO

Please I need ASAP thank you very much

Answers

Answer:

a. 0= 3^3-2(3)^2-2(3)-3

(set the equation to zero. x=3, so plug 3 into all of the x's ^^)

27-18-6-3

(do all of the multiplying and stuff ^^)

0

(combine like terms ^^)

Step-by-step explanation:

i hope this helps!!

What number minus one-half is equals to negative one-half

Answers

Answer:

0

Step-by-step explanation:

At Smith's Sporting Goods,3 out of every 10 customers make a purchase. Write a ratio to compare the number of customers who make a purchase to the number of customers who do not make a purchase.

Answers

Answer:

30

Step-by-step explanation:

because 3×10 is 30 and so 3 out of 10 is 30

Write the phrase as an expression. Then evaluate the expression when y=20 . the quotient of 40 and the difference of a number y and 16 Expression: When y=20, the value of the expression is

Answers

Answer:

Write the phrase as an expression. Then evaluate the expression when y=20 . the quotient of 40 and the difference of a number y and 16 Expression: When y=20, the value of the expression is

What is the value of the expression - 1.76 • 1/5 • (- 3.6)? Enter your answer below.

Answers

Answer:

-9.504

Step-by-step explanation:

First you do 1.76 times 1.5 which is 2.64. Then you do 2.64 times negative 3.6 which would be -9.504.

Answer:

Step-by-step explanation:

brooooooooo wtfffffffff

Please help I’ll mark your brainlist!

Answers

Answer:

D f(x) = 4X - 3

Step-by-step explanation:

If you substitute the numbers of the table into the equation it works out, for example

2 x 4 = 8 - 3 = 5

3 x 4 = 12 - 3 = 9

4 x 4 = 16 - 3 = 13

what is -3 take away -1?

Answers

the answer to the question is -2

A glacier moves about 3 inches every 9 hours. At this rate, about how far does the glacier move in 36 hours?
Help me please

Answers

Answer:

The answer is 12

Step-by-step explanation:

36/9=4

4x3=12

So first you would divide 12 in half to figure out how many inches it moves in 24 hours (or 1 day) which would be 6 inches every 24 hours. You then multiply 6 (inches per day) by 7 (# of days). You end up with 42 inches in 7 days. Hope this helps

Which of the following shows the correct solution steps amd solution to 7x-4=-18

Answers

Answer:

D

Step-by-step explanation:

7x - 4 = -18            (add 4 to both sides)

7x = -14                  (divide both sides by 7)

x = -2

the answer is D

The cost for an eighth-grade party is $450 for room rental, entertainment, and
decorations, plus $20 per person for food. Tickets for the party are sold for $25. What is
the break-even point?

Answers

how many people????????????

The first transformation for this composition is [________], and the second transformation is a translation down and to the right. a 90° rotation about point L a 270° rotation about point L a 90° rotation about point P a 270° rotation about point P

Answers

Answer:

D. A 270-degree rotation about point P

Step-by-step explanation:

I hope this helps!!!

what is 287.5/25 simplified I’m literally close to tears help

Answers

Answer:

11.5

Step-by-step explanation:

I hope this helps :)

Answer:

11.5

Step-by-step explanation:

have a great day <3

PLEASE HELP ASAP WILL GIVE BRAINLEST!!!!

In ΔPQR, what is the m∠Q? Enter your answer in the box.


m∠Q=

Answers

Answer:

105

Step-by-step explanation:

all of the angles added will add up to equal 180 so we setup the equation

180=11x-5+6x+5+x and solve

step 1 combine like terms

180=18x

step 2

divide each side by 18

x=10

then we just plug in 10 to 11x-5

11x10=110-5=105

angle q=105

What is an expression equivalent to 6 - 4(3 - 6m) + 12m that is the product of two factors.​

Answers

Answer:

36m-6

If im wrong im sorry

PLEASE HELP!!!!!!!
What is the area of this figure?

28 yd²

40 yd²

52 yd²

64 yd

Answers

Answer:

40yd

Step-by-step explanation:

Answer:

i got 28 yd2

Step-by-step explanation:

for the triangle: 6×4= 24, but since a triangle is half divide by 2

24/2=12

4×4= 16

12+16= 28

lmk if I'm wrong, i might be a little rusty

Determine which function(s) are exponential. Select all that apply.

Answers

Answer:

option B and option C represent an exponential function.

Step-by-step explanation:

We know that following are some of the properties of different functions.

Linear Function:

The constant change in x and y

Quadratic Function:

The constant change in x

The constant 2nd differences in y

Exponential Function:

The constant change in x

The constant ratio in y

Determining the nature of the exponential function

Option A)

x       0          1          2         3           4

y       0          1           4         9          16

Here:

There is a constant change in x:

1 - 0 = 1;  2 - 1 = 1;  3 - 2 = 1;  4 - 3 = 1

BUT, there is NO CONSTANT ratio, as

1/0 = ∞,  4/1 = 4,  9/4 ; 16/9

Thus,

Table A DOES NOT represents an exponential function.

Option B)

x       0          1          2         3           4

y       1/3        1           3        9           27

Here:

There is a constant change in x:

1 - 0 = 1;  2 - 1 = 1;  3 - 2 = 1;  4 - 3 = 1

There is also a constant ratio, as

1/[1/3] = 3,  3/1 = 3,  9/3 = 3; 27/9 = 3

As there is constant change in x as well a constant ratio.

Thus,

Table B REPRESENTS an exponential function.

Option C)

x       0          1          2         3           4

y       5          5/2      5/4      5/8       5/16

Here:

There is a constant change in x:

1 - 0 = 1;  2 - 1 = 1;  3 - 2 = 1;  4 - 3 = 1

There is also a constant ratio, as

[5/2]/5= 1/2,

[5/4]/[5/2] = 1/2

[5/8]/[5/4] = 1/2

[5/16]/[5/8] = 1/2

As there is constant change in x as well a constant ratio.

Thus,

Table C REPRESENTS an exponential function.

Option D)

x       0          1          2         3           4

y       4.5       4        3.5       3          2.5

Here:

There is a constant change in x:

1 - 0 = 1;  2 - 1 = 1;  3 - 2 = 1;  4 - 3 = 1

BUT, there is NO CONSTANT ratio, as

4/4.5 = 4/[45/10] = 40/45 = 8/9

3.5/4 = [35/10]/4 = 35/40 = 7/8

3/3.5 = 3/[35/10] = 30/35 = 6/7

2.5/3 = [25/10]/3 = 25/30 = 5/6

Table D  DOES NOT represent an exponential function.

Conclusion:

Therefore, option B and option C represent an exponential function.

The functions that are exponential would be:

B). [tex]x[/tex]   0          1          2         3           4

   [tex]y[/tex]     1/3        1           3        9          27

C). [tex]x[/tex]       0          1          2         3           4

      [tex]y[/tex]     5          5/2      5/4      5/8       5/16

What are Exponential Functions?

B). Given that,

[tex]x[/tex]   0          1          2         3           4

 [tex]y[/tex]     1/3        1           3        9          27

As we see,

The value of [tex]x[/tex] undergoes a constant change of 1

[tex]1 - 0 = 1; \\2 - 1 = 1; \\3 - 2 = 1; \\4 - 3 = 1[/tex]

The ratio also remains constant

[tex]1/[1/3] = 3, \\3/1 = 3, \\9/3 = 3; \\27/9 = 3[/tex]

Thus, it exemplifies an exponential function.

Similarly,

C). [tex]x[/tex]       0          1          2         3           4

      [tex]y[/tex]     5          5/2      5/4      5/8       5/16

As we see,

The value of [tex]x[/tex] undergoes a constant change of 1

[tex]1 - 0 = 1; \\2 - 1 = 1; \\3 - 2 = 1; \\4 - 3 = 1[/tex]

The ratio also remains constant

[tex][5/2]/5= 1/2\\\\[5/4]/[5/2] = 1/2\\\\[5/8]/[5/4] = 1/2\\\\[5/16]/[5/8] = 1/2[/tex]

Thus, it exemplifies an exponential function.

Thus, options B and C are the correct answers as the other two have a constant change but not a constant ratio.

Learn more about "exponential function" here:

brainly.com/question/15352175

Please help!!! Graph the line with slope −1 and y-intercept 3

Answers

This is what I got when i graphed it.

HI I NEED HELP WITH THIS!!! SOMEONE ANSWER ASAP PLS

Answers

10
the hypotenuse is the largest side
so out of 6,8,10
10 is the largest

Evaluate help please!

Answers

ABSOLUTE VALUE

The absolute value of a number is the distance from 0 to that number. The distance is positive, hence, the absolute value is always a positive number.

Exercise

Replace the value of x:

[tex]| x - 8 |[/tex]

[tex]| -4 - 8 |[/tex]

[tex]| -12 | = \large{\boxed{12}}[/tex]

The absolute value of a number is the numerical value of the number, without regard to its sign.

Answer. 12

Evaluate the following expression if x = 3. x2

Answers

Answer:

6

Step-by-step explanation:

x2

x=3

sub 3 into x

(3)2

=6

Plot the image of point D under a dilation about the origin (0,0) with a scale factor of 2.

Answers

Answer:

I think it is -3,-2.......

Please help me this is due in and hour

Answers

Answer:

The answer is All Solution

Step-by-step explanation:

Shaggy earned 7.50 an hour plus an additional $100 in tips waiting tables last night. He earned more than $160 in all. Write an inequality to represent this situation and help you find the number of hours (h) he worked.

Answers

Answer

x>21.2

Step-by-step explanation:

7.55x+100>160:

subtract 100 on both sides to get:

7.55x>60:

divide 7.55 on both sides:

x>21.2 is your answer  

 

Answer:

7.50h + 100 > 160

Step-by-step explanation:

7.50 is the hourly wage

h = hours he worked

add 100 once because it's his tips for the amount of time her worked

since he worked more than 160, you'll use the greater sign

then solve for h

h = 8 hours

mr.torres is 6 1/4 feet tall. Mr. torres is 5 1/2 feet tall. How much shorter is Mrs. torres than her husband PLEASE HURRY!

Answers

Answer: 3/4

Step-by-step explanation: 6 1/4 - 5 1/2

Answer: The answer is 1 2/8

Step-by-step explanation:

5 1/2    X    4/4     =   4/8               So the answer is 1 and 2/8

6 1/4     X   2/2     =   2/8

6 4/8

-

5 2/8

___

1  2/8  

determine an equation of a line in standard form that is perpendicular lo the line 2y = -x + 3 and passes through the point (4, 5).​

Answers

first, i put the equation in y=mx+b by dividing 2, since its 2y. since it’s perpendicular we’re talking about you switch the sides (opposite reciprocals). the rest should be self explanatory.

Offering Brainleast if you explain your answer

Answers

In order to answer you would have to plug 62 in the x spot and then make it equal to 180

Please find the solution to the following system using substitution or elimination: y = -2x + 7 y = 3x - 8

Answers

Answer:

This is improper ma'am or sir , there is to many equal sighns , is there a mistake

Step-by-step explanation:

y= 7 x 3 +8           or     x =3 y 7 −24 7

(Sorry if its wrong )

Problem 2
A jewelry store purchased a pair of earrings for $54
before a markup was applied.
There was a 90% markup. After the markup, a 6.5%
sales tax is added.
What is the total after markup and tax?

Answers

Answer:

$109.27

Step-by-step explanation:

100 + 90 = 190

54/100 X 190 = 102.60

100 + 6.5 = 106.5

102.60/100 X 106.5 = 109.269

monetary unit round to 2dp

109.27

Helppppppppp fasttttttt pleaseeeeeee!!!!!!!

Answers

Answer:

(3x⁷)⁴ = 3⁴x²⁸ = 81x²⁸

because (3x⁷)⁴ = cx^n

=> c = 81

n = 28

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