Problem
Using a double-angle or half-angle formula to simplify the given expressions. (a) If $\cos ^{2}\left(26^{\circ}\right)-\sin ^{2}\left(26^{\circ}\right)=\cos \left(A^{\circ}\right)$, then \[ A= \] degrees. (b) If $\cos ^{2}(8 x)-\sin ^{2}(8 x)=\cos (B)$, then \[ B= \]
Solution
Step 1 ：The double angle formula for cosine is \(\cos(2\theta) = \cos^2(\theta) - \sin^2(\theta)\). This means that the given expression \(\cos^2(26^{\circ}) - \sin^2(26^{\circ})\) is equivalent to \(\cos(2*26^{\circ})\). Therefore, A = 2*26^{\circ}.
Step 2 ：Final Answer: \(A = \boxed{52}\)
