Use a power-reducing identity to rewrite the following expression below in terms containing only first powers of sine and cosine.sin3(x)
Question
Use a power-reducing identity to rewrite the following expression below in terms containing only first powers of sine and cosine.
sin^3(x)
Solution
The power-reducing identities are:
sin²(x) = 1/2 - 1/2 cos(2x) cos²(x) = 1/2 + 1/2 cos(2x)
However, your expression is sin³(x), not sin²(x). To rewrite sin³(x) in terms of first powers of sine and cosine, we can use the identity sin³(x) = (3sin(x) - sin(3x))/4.
So, sin³(x) can be rewritten as (3sin(x) - sin(3x))/4.
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