Question

6 sin 2 ⁡ x + 4 cos 2 ⁡ x ≡ A + B cos 2 ⁡ x where A and B are integers. Work out the values of A and B .

Answer 1

$\textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta) \\\\[-0.35em] ~\dotfill\\\\ 6sin^2(x)+4cos^2(x)\implies 6[~1-cos^2(x)~]+4cos^2(x) \\\\\\ 6-6cos^2(x)+4cos^2(x)\implies \stackrel{A}{6}~~ \stackrel{B}{-2}cos^2(x)$