question 17 of 20 cos2a = 2cos²a - 1 for all values of a. a. true b. false
question 17 of 20 cos2a = 2cos²a - 1 for all values of a. a. true b. false
Answer
Answer:
A. True
Explanation:
Step1: Recall double - angle formula
The double - angle formula for cosine is $\cos2\alpha=\cos^{2}\alpha-\sin^{2}\alpha$.
Step2: Use trigonometric identity
Since $\sin^{2}\alpha = 1-\cos^{2}\alpha$, substitute it into the double - angle formula. Then $\cos2\alpha=\cos^{2}\alpha-(1 - \cos^{2}\alpha)$.
Step3: Simplify the expression
$\cos2\alpha=\cos^{2}\alpha-1+\cos^{2}\alpha=2\cos^{2}\alpha - 1$. So $\cos2\alpha = 2\cos^{2}\alpha-1$ for all values of $\alpha$.