Question

Rewrite the given function as an equivalent function containing only cosine terms raised to a power of 1.f(x)=7cos^2x

Answer 1

Explanation:

Using the double angle formulas,

cos(2x) = cos^2(x) - sin^2(x) ............(1)

1 = cos^2(x) + sin^2(x)............(2)

add (1) and (2)

1 + cos(2x) = 2 cos^2(x)

=> cos^2(x) = (1/2) (1+cos(2x)) ..............(3)

f(x) = 7 cos^2 (x)

substituting (3)

f(x) = (7/2) (1+cos(2x))