Question

prove that cos24 + Cos155 + Cos25 + Cos204 = 0
​

Answer 1

$\textbf{To prove:}$

$\mathsf{cos24^\circ+cos155^\circ+cos25^\circ+cos204^\circ=0}$

$\textbf{Solution:}$

$\mathsf{Consider,}$

$\mathsf{cos24^\circ+cos155^\circ+cos25^\circ+cos204^\circ}$

$\mathsf{=cos24^\circ+cos(180^\circ-25^\circ)+cos25^\circ+cos(180^\circ+24^\circ)}$

$\mathsf{Using,}$

$\boxed{\mathsf{cos(180^\circ-\theta)=-cos\theta}}$

$\boxed{\mathsf{cos(180^\circ+\theta)=-cos\theta}}$

$\mathsf{=cos24^\circ-cos25^\circ+cos25^\circ-cos24^\circ}$

$\implies\boxed{\mathsf{cos24^\circ+cos155^\circ+cos25^\circ+cos204^\circ=0}}$

$\textbf{Find more:}$

cos 12 cos 24 cos 36 cos 48 Cos 60 cos 72 cos 84 equal = 1 / 128​

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Prove that cos20.cos40.cos80=1/8

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