Question

Use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine. sin⁴ x

Answer 1

To rewrite sin⁴ x in terms of the first power of cosine, use the identity sin² x = 1 - cos² x. Manipulate the expression to get 1 - 2cos² x + cos⁴ x.

Step-by-step explanation:

To rewrite the expression sin⁴ x in terms of the first power of cosine, we can use the identity sin² x = 1 - cos² x. Let's manipulate the expression:

sin⁴ x = (sin² x)² = [(1 - cos² x)²] = (1 - cos² x) (1 - cos² x) = 1 - 2cos² x + cos⁴ x

Therefore, the expression sin⁴ x in terms of the first power of cosine is 1 - 2cos² x + cos⁴ x.