write the expression as a product of trigonometric functions. \n sin 17° + sin (-54°) \n sin 17° + sin…

write the expression as a product of trigonometric functions. \n sin 17° + sin (-54°) \n sin 17° + sin (-54°) = \n (use integers or fractions for any numbers in the expression. do not include the degree symbol in your answ

write the expression as a product of trigonometric functions. \n sin 17° + sin (-54°) \n sin 17° + sin (-54°) = \n (use integers or fractions for any numbers in the expression. do not include the degree symbol in your answ

Answer

Explanation:

Step1: Use the sum - to - product formula

The sum - to - product formula for (\sin A+\sin B = 2\sin\frac{A + B}{2}\cos\frac{A - B}{2}). Here (A = 17) and (B=-54).

Step2: Calculate (\frac{A + B}{2}) and (\frac{A - B}{2})

First, (\frac{A + B}{2}=\frac{17+( - 54)}{2}=\frac{17 - 54}{2}=\frac{-37}{2}). Second, (\frac{A - B}{2}=\frac{17-( - 54)}{2}=\frac{17 + 54}{2}=\frac{71}{2}).

Step3: Substitute into the formula

(\sin17+\sin(-54)=2\sin\frac{17+( - 54)}{2}\cos\frac{17-( - 54)}{2}=2\sin\left(-\frac{37}{2}\right)\cos\frac{71}{2}). Since (\sin(-x)=-\sin x), we can rewrite it as (- 2\sin\frac{37}{2}\cos\frac{71}{2}).

Answer:

(-2\sin\frac{37}{2}\cos\frac{71}{2})