Question

- Express sin 120 + sin 40 as the product of sines and cosines.​

Answer 1

Answer 2sin80cos40

Step-by-step explanation:

Re call the formula: sinx+ siny

= 2sin (x+y/2).cos (x-y/2)

Answer 2

The correct answer is 2sin(80)cos(40).

Given:

sin 120 + sin 40

To find:

sin 120 + sin 40 as product of sines and cosines.

Solution:

Sine and cosines are trigonometric ratios which have some identities and formulae.

One of them is sin(A) + sin(B)

The formula for sin(A) + sin(B) is given by,

sin(A) + sin(B) = $2 sin (\frac{A+B}{2}) cos \frac{(A-B)}{2}$

According to question,

A = 120

B = 40

So,

sin 120 + sin 40 = $2 sin (\frac{120+40}{2}) cos \frac{(120-40)}{2}$

sin 120 + sin 40 = 2 sin (80) cos(40)

Hence, in terms of product of sines and cosines, we can express

sin 120 + sin 40 as 2 sin (80) cos(40).

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