question 0 of 20 cos2a =1 - 2sin² a for all values of a. a. true b. false
question 0 of 20 cos2a =1 - 2sin² a 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 $\cos2a=\cos^{2}a - \sin^{2}a$.
Step2: Use Pythagorean identity
Since $\cos^{2}a=1 - \sin^{2}a$, substitute it into the double - angle formula: $\cos2a=(1 - \sin^{2}a)-\sin^{2}a$.
Step3: Simplify the expression
$\cos2a = 1-2\sin^{2}a$. So the statement is true for all values of $a$.