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Question

α=sin1(cos(sin1x)) and β=cos1(sin(cos1x)) then:

A
tanα=cotβ
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B
tanα=cotβ
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C
tanα=tanβ
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D
tanα=tanβ
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Solution

The correct option is A tanα=cotβ
α=sin1(cos(sin1(x))))
=π2cos1(cos(π2cos1(x)))
=π2cos1(sin(cos1(x)))
=π2β
Hence α=π2β
Hence tan(α)=cot(β)

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