Use a producttosum indentity to rewrite the expression 9cos

Use a product-to-sum indentity to rewrite the expression.

9cos v sin8v

(Use integers or fractions for any numbers in the expression.)

Solution

9cosv*sin8v

Using the standard sum formula : cosa*sinb = (1/2) { sin( a+b) - sin( a-b) }

In our case : 9cosv*sin8v

a = v and b = 8v

9cosv*sin8v = 9(1/2) { sin( v +8v) -sin( v -8v) }

= (9/2) { sin9v +sin7v }