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Question: If \(\Rightarrow x = 2n\pi \pm \cos^{- 1}(1/3)\), then the general value of \(\cos\theta + \cos 2\th...

If ⇒x=2nπ±cos⁡−1(1/3)\Rightarrow x = 2n\pi \pm \cos^{- 1}(1/3), then the general value of cos⁡θ+cos⁡2θ+cos⁡3θ=0\cos\theta + \cos 2\theta + \cos 3\theta = 0 will be in.

A

A. P.

B

G. P.

C

H. P.

D

None of these

Answer

A. P.

Explanation

Solution

3sin⁡(A−15o)cos⁡(A−15o)=sin⁡(A+15o)cos⁡(A+15o)3sin⁡(A−15o)cos⁡(A+15o)\frac{3\sin(A - 15^{o})}{\cos(A - 15^{o})} = \frac{\sin(A + 15^{o})}{\cos(A + 15^{o})}3\sin(A - 15^{o})\cos(A + 15^{o}) =cos⁡(A−15o)sin⁡(A+15o)= \cos(A - 15^{o})\sin(A + 15^{o})

Hence different values of ⇒\Rightarrow are in A.P. with 2sin⁡(A−15o)cos⁡(A+15o)=122\sin(A - 15^{o})\cos(A + 15^{o}) = \frac{1}{2} as common difference.