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Question

If α=cos-135,β=tan-113, where 0<α,β<π2, then α-β is equal to:


A

tan-19510

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B

sin-19510

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C

tan-1915

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D

cos-19510

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Solution

The correct option is B

sin-19510


Find the value of α-β:

Given,

α=cos-135=tan-143

β=tan-113

α-β=tan-143tan-113

=tan-143-131+43×13 tan-1A-tan-1B=tan-1(A-B1+AB)

=tan-111+49

=tan-1913

=sin-19132+92 tan-1(AB)=sin-1(1A2+B2)

=sin-19250

=sin-1(9510)

Hence, Option ‘B’ is Correct.


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