Q.

If  cos(θα),cosθ,cos(θ+α) are in H.P. then   |cosθ.secα2|2=

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answer is 2.

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Detailed Solution

Apply H.P. condition  

2cosθ=1cos(θα)+1cos(θ+α)2cosθ=cos(θ+α)+cos(θa)cos(θα)cos(θ+α)2cosθ=2coscosαcos2θsin2αcos2θsin2α=cos2θcosαcos2θ[1cosα]=sin2α

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If  cos(θ−α),cosθ,cos(θ+α) are in H.P. then   |cosθ.secα2|2=