write the expression as a sum or difference of trigonometric functions. 4 sin 2x sin 6x 4 sin 2x sin 6x =
write the expression as a sum or difference of trigonometric functions. 4 sin 2x sin 6x 4 sin 2x sin 6x =
Answer
Explanation:
Step1: Use the product - to - sum formula
The product - to - sum formula for (\sin A\sin B) is (\sin A\sin B=\frac{1}{2}[\cos(A - B)-\cos(A + B)]). Here (A = 2x) and (B=6x). So, (4\sin2x\sin6x=4\times\frac{1}{2}[\cos(2x - 6x)-\cos(2x + 6x)])
Step2: Simplify the expression
First, simplify (4\times\frac{1}{2}=2). Then, simplify the arguments of the cosine functions: (2x-6x=-4x) and (2x + 6x=8x). Since (\cos(-\alpha)=\cos\alpha), the expression becomes (2[\cos4x-\cos8x]=2\cos4x-2\cos8x)
Answer:
(2\cos4x - 2\cos8x)