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
\[
B=
\]

Answer

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Answer

Final Answer: $A = \boxed{52}$

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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: $A = \boxed{52}$

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\[B=\]

Answer

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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
\[
B=
\]