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Prove that: ...

Question

Prove that: $2 cos x - cos 3 x - cos 5 x = 16 {cos}^{2} x {sin}^{2} x$

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Solution

RHS $= 2 cos x - 2 cos 4 x cos x = 2 cos x (1 - cos 4 x) = 2 cos x .2 {sin}^{2} 2 x = 4 cos x {(2 sin x cos x)}^{2} = 16 {cos}^{3} x {sin}^{2} x$

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\frac{cos 5 x + cos 4 x}{2 cos 3 x - 1} = cos x + cos 2 x

\frac{sin 5 x + sin 3 x}{cos 5 x + cos 3 x} = tan 4 x

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