Question

question 9 (1 point)
which compound angle formula is the easiest to use to develop the expression (cos^{2}\theta-sin^{2}\theta)?
a) subtraction formula for sine
b) addition formula for sine
c) subtraction formula for cosine
d) addition formula for cosine

Explanation:

Step1: Recall addition formula for cosine

The addition formula for cosine is \(\cos(A + B)=\cos A\cos B-\sin A\sin B\).

Step2: Let \(A = B=\theta\)

Substitute \(A = B=\theta\) into the formula: \(\cos(\theta+\theta)=\cos\theta\cos\theta-\sin\theta\sin\theta\).

Step3: Simplify

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

Answer:

d) addition formula for cosine