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If $\cos (x - y), \cos x and \cos (x + y)$ are in H.P., then $|\cos x \sec \frac{y}{2}|$ equal to

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Correct option is C

It is given that cos⁡(x−y),cos⁡x and cos⁡(x+y) are in H.P∴ 2cos⁡x=1cos⁡(x−y)+1cos⁡(x+y)⇒ 2cos⁡x=2cos⁡xcos⁡ycos2⁡x−sin2⁡y⇒ cos2⁡xcos⁡y=cos2⁡x−sin2⁡y⇒ cos2⁡x(1−cos⁡y)=sin2⁡y⇒ 2cos2⁡xsin2⁡y2=4sin2⁡y2cos2⁡y2⇒ cos2⁡xsec2⁡y2=2⇒ cos⁡xsec⁡y2∣=2

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