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Question

If tan β=n sin α cos α1n sin2 α, then tan (αβ)is equal to


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


tan β=n ta α1+tan2α+n tan2 α=n tan α1+(1n)tan2α=tan(αβ)=tan αn tan α1+(1n)tan2α1+tan α, n tan α1+(1n)tan2α=tan α(1n)tan3αn tan α1+(1n)tan2α+n tan2α=(1n)tan α(1+tan2α)1+tan2α=(1n)tan α


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