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Question

If cos θ+{sin θ+sin2 θ+sin2 α}k, then the value of k is


A

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B

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C

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D

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Solution

The correct option is B


Let u=cos θ{sin θ+sin2 θ+sin2α} (usinθ cosθ)2=cos2 θ(sin2 θ+sin2 α) u2 tan2 θ2u tan θ+u2sin2 α=0Since tan θ is real, therefore4u24u2(u2sin2 α)0u2(1+sin2 α)0|u|1+sin2 α


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