If $$cos$$⁡$$($$θ−α$$)$$,$$cos$$⁡θ,$$cos$$⁡$$($$θ$$+$$α$$)$$ are in H.P., then $$cos$$⁡θ$$sec$$⁡$$($$α$$/2)is$$ equal to

Question

If $$cos$$⁡$$($$θ−α$$)$$,$$cos$$⁡θ,$$cos$$⁡$$($$θ$$+$$α$$)$$ are in H.P., then $$cos$$⁡θ$$sec$$⁡$$($$α$$/2)is$$ equal to

Infinity Learn · Accepted Answer

We are given that $$cos$$⁡θ$$=2cos$$⁡$$($$θ−α$$)$$$$cos$$⁡$$($$θ$$+$$α$$)$$$$cos$$⁡$$($$θ−α$$)+$$$$cos$$⁡$$($$θ$$+$$α$$)$$⇒ $$cos$$⁡θ$$=2cos2$$⁡θ−$$sin2$$⁡α$$2cos$$⁡θ$$cos$$⁡α⇒ $$cos2$$⁡θ$$cos$$⁡α$$=cos2$$⁡θ−$$sin2$$⁡α⇒ $$cos2$$⁡θ$$=sin2$$⁡α$$1$$−$$cos$$⁡α⇒ $$cos$$⁡θ$$=4sin2$$⁡α$$2cos2$$⁡α$$22sin2$$⁡α$$2$$⇒ $$cos2$$⁡θ$$sec2$$⁡α$$2=2$$⇒$$cos$$⁡θ$$sec$$⁡α$$2=$$±$$2$$

If $\cos (θ - α), \cos θ, \cos (θ + α)$ are in H.P., then $\cos θ \sec (α / 2)$ is equal to

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If cos⁡(θ−α),cos⁡θ,cos⁡(θ+α) are in H.P., then cos⁡θsec⁡(α/2)is equal to

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If $\cos (θ - α), \cos θ, \cos (θ + α)$ are in H.P., then $\cos θ \sec (α / 2)$ is equal to