Question

Use a power reducing formula to simplify 16sin4t. write your answer as an equivalent expression that does not contain any powers of sine or cosine greater than 1.

a. 16sin(4t)
b. 8sin²(2t)
c. 8cos²(2t)
d. 16cos(4t)

Answer 1

To simplify 16sin4t using a power reducing formula, rewrite sin(4t) as sin^2(2t) using the double angle identity and then simplify the expression.

Step-by-step explanation:

To simplify 16sin4t using a power reducing formula, we can use the identity sin^2(x) = (1 - cos(2x))/2. Since we have sin(4t), we can rewrite it as sin^2(2t) using the double angle identity. Therefore, the expression becomes 16(1 - cos(4t))/2. Simplifying further, we get 8(1 - cos(4t)). Hence, the answer is 8(1 - cos(4t)).

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