Question

Use a double angle, half angle, or power reduction formula to rewrite without exponents. a. cos^2(5x)

a) 1/2+ 1/2 cos(10x)
b) cos(10x)
c) 1/2cos(5x)
d) 1/2cos(10x)

Answer 1

To rewrite cos^2(5x) without exponents, we use the power reduction formula cos^2(θ) = (1 + cos(2θ))/2, resulting in (1 + cos(10x))/2, which is option (a).

Step-by-step explanation:

To rewrite cos2(5x) without exponents using a power reduction formula, we refer to one of the trigonometric identities:

cos2(θ) = (1 + cos(2θ))/2

Applying this identity to cos2(5x), we get:

cos2(5x) = (1 + cos(10x))/2

This means that the correct option to rewrite cos2(5x) without exponents is (a) 1/2 + 1/2 cos(10x).