Problem

Expand \(\cos^2x\) using double-angle formulas.

Answer

Expert–verified
Hide Steps
Answer

We need to express \(\cos^2x\) in terms of \(\cos 2x\), so we rearrange the second double-angle formula to solve for \(\cos^2x\): \(\cos^2x = \frac{\cos2x + 1}{2}\)

Steps

Step 1 ：First, recall the double-angle formula for cosine: \(\cos2x = 1 - 2\sin^2x\) or \(\cos2x = 2\cos^2x - 1\).

Step 2 ：We need to express \(\cos^2x\) in terms of \(\cos 2x\), so we rearrange the second double-angle formula to solve for \(\cos^2x\): \(\cos^2x = \frac{\cos2x + 1}{2}\)

link_gpt

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find $y^{\prime}$ if $y=\ln \… 3. (3pts) Cherry trees in a c… More