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Using a double-angle or half-angle formula to simplify the given expressions. (a) If cos^(2)(22^(@))-sin^(2)(22^(@))=cos(A^(@)), then A= ◻ degrees. (b) If cos^(2)(9x)-sin^(2)(9x)=cos(B), then B= ◻

Using a double-angle or half-angle formula to simplify the given expressions.\newline(a) If cos⁡2(22∘)−sin⁡2(22∘)=cos⁡(A∘) \cos ^{2}\left(22^{\circ}\right)-\sin ^{2}\left(22^{\circ}\right)=\cos \left(A^{\circ}\right) , then\newlineA= A= \newline□ \square degrees.\newline(b) If cos⁡2(9x)−sin⁡2(9x)=cos⁡(B) \cos ^{2}(9 x)-\sin ^{2}(9 x)=\cos (B) , then\newlineB= B= \newline□ \square

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Full solution

Q. Using a double-angle or half-angle formula to simplify the given expressions.\newline(a) If cos⁡2(22∘)−sin⁡2(22∘)=cos⁡(A∘) \cos ^{2}\left(22^{\circ}\right)-\sin ^{2}\left(22^{\circ}\right)=\cos \left(A^{\circ}\right) , then\newlineA= A= \newline□ \square degrees.\newline(b) If cos⁡2(9x)−sin⁡2(9x)=cos⁡(B) \cos ^{2}(9 x)-\sin ^{2}(9 x)=\cos (B) , then\newlineB= B= \newline□ \square
  1. Apply double-angle formula: Use the double-angle formula for cosine, which states cos⁡(2θ)=cos⁡2(θ)−sin⁡2(θ)\cos(2\theta) = \cos^2(\theta) - \sin^2(\theta). Apply this to simplify cos⁡2(22∘)−sin⁡2(22∘)\cos^2(22^\circ) - \sin^2(22^\circ).
  2. Simplify expression using formula: For the second expression, apply the same double-angle formula to cos⁡2(9x)−sin⁡2(9x)\cos^2(9x) - \sin^2(9x).

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