Question

complete the sentence below.
cos (2θ)=cos²θ - ____ = __ - 1 = 1 - ____.
cos (2θ)=cos²θ - □ = □ - 1 = 1 - □

Explanation:

Step1: Use the double - angle formula for cosine

The double - angle formula for cosine is \(\cos(2\theta)=\cos^{2}\theta-\sin^{2}\theta\).

Step2: Use the Pythagorean identity \(\sin^{2}\theta = 1-\cos^{2}\theta\)

Substitute \(\sin^{2}\theta\) into the formula \(\cos(2\theta)=\cos^{2}\theta-(1 - \cos^{2}\theta)=2\cos^{2}\theta-1\).

Step3: Use the Pythagorean identity \(\cos^{2}\theta=1 - \sin^{2}\theta\)

Substitute \(\cos^{2}\theta\) into the formula \(\cos(2\theta)=1-2\sin^{2}\theta\).

Answer:

\(\cos(2\theta)=\cos^{2}\theta-\sin^{2}\theta = 2\cos^{2}\theta-1=1 - 2\sin^{2}\theta\)