rewrite the expression in terms of the first power of cosine.
cos^3(x)sin^4(x)
To rewrite the expression cos^3(x)sin^4(x) in terms of the first power of cosine, we can use the identities:
sin^2(x) = 1 - cos^2(x) (Pythagorean identity)
sin^4(x) = (sin^2(x))^2 = (1 - cos^2(x))^2
Substituting the value of sin^4(x) in the expression:
cos^3(x)sin^4(x) = cos^3(x)(1 - cos^2(x))^2
Expanding the expression (1 - cos^2(x))^2 using the binomial expansion:
(1 - cos^2(x))^2 = (1 - 2cos^2(x) + cos^4(x))
Therefore, the expression cos^3(x)sin^4(x) in terms of the first power of cosine is:
cos^3(x)sin^4(x) = cos^3(x)(1 - 2cos^2(x) + cos^4(x))