Question

write the expression as a sum or difference of trigonometric functions. 2 sin 48° cos 96° 2 sin 48° cos 96° = (do not include the degree symbol in your answer.)

Explanation:

Step1: Use the product - to - sum formula

The formula \(2\sin A\cos B=\sin(A + B)+\sin(A - B)\). Here \(A = 48\) and \(B=96\).

Step2: Calculate \(A + B\) and \(A - B\)

\(A + B=48+96 = 144\) and \(A - B=48 - 96=-48\).

Step3: Substitute into the formula

Since \(\sin(-x)=-\sin x\), then \(2\sin48\cos96=\sin144+\sin(-48)=\sin144-\sin48\).

Answer:

\(\sin144-\sin48\)