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Question

If cos xsinαcotβsin x=cosα ,
then the value of tan(x2) is

A
tan(α2)cot(β2)
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B
tan(α2)tan(β2)
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C
cot(α2)tan(β2)
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D
cot(α2)tan(β2)
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Solution

The correct options are
A tan(α2)cot(β2)
B tan(α2)tan(β2)

The given equation can be written as
1tan2(x2)1+tan2(x2)sinα cotβ2tan(x2)1+tan2(x2)=cosαtan2x2(1+cosα)+sinα cotβ.2tanx2(1cosα)=0tan2x2+2sinαcotβ1+cosαtanx21cosα1+cosα=0tan2x2+2tanα2cotβtanx2tan2α2=0tan2x2+2tanα2.12(cotβ2tanβ2)tanx2tan2α2=0(tanx2+cotβ2tanα2)(tanx2tanβ2tanα2)=0tan(x2)=tan(α2)cot(β2) or tan(x2)=tan(α2)tan(β2)


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