Use the producttosum identities to rewrite the expression s

Use the product-to-sum identities to rewrite the expression. ( sin sin 10 | sin | T Which of the following is equivalent to sin ? 10 OA. 1( 7x 2 13x 30 coscos cos cos 30 k to select your answer

Solution

We know that
cos(a+b) = cosacosb - sinasinb

cos(a-b) = cosacosb + sinasinb

Subtractin em :
cos(a-b) - cos(a+b) = 2sinasinb

So, sinAsinB =
[cos(A-B) - cos(A+B)] / 2

Now, plug in pi/3 and pi/10 ;
cos(pi/3-pi/10) - cos(pi/3+pi/10) / 2

1/2 * [cos(7pi/30) - cos(13pi/30)] ---> ANS

Same as option A except a minus in between