Question

assignment 7.3: double - angle, half - angle, and reduction for
score: 20/80 answered: 1/3
question 2
using a double - angle or half - angle formula to simplify the given expressions.
(a) if cos²(33°) - sin²(33°) = cos(a°), then
a =
degrees.
(b) if cos²(9x) - sin²(9x) = cos(b), then
b =
question help: worked example 1 post to forum
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Explanation:

Step1: Recall double - angle formula

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

Step2: Solve for part (a)

Given $\cos^{2}(33^{\circ})-\sin^{2}(33^{\circ})=\cos(A^{\circ})$. By the double - angle formula $\cos(2\theta)=\cos^{2}\theta-\sin^{2}\theta$, when $\theta = 33^{\circ}$, we have $A = 2\times33=66$.

Step3: Solve for part (b)

Given $\cos^{2}(9x)-\sin^{2}(9x)=\cos(B)$. By the double - angle formula $\cos(2\theta)=\cos^{2}\theta-\sin^{2}\theta$, when $\theta = 9x$, we have $B = 2\times9x = 18x$.

Answer:

(a) $66$
(b) $18x$