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Question

If α=cos1(35),β=tan1(13), where 0<α,β<π2, then αβ is equal to:

A
tan1(914)
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B
sin1(9510)
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C
cos1(9510)
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D
tan1(9510)
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Solution

The correct option is B sin1(9510)
Given,
α=cos1(35)=tan1(43)
β=tan1(13)

Now,
αβ=tan1(43)tan1(13)
=tan1⎜ ⎜ ⎜43131+4313⎟ ⎟ ⎟

=tan1(913)

=sin1(9250)

=sin1(9510)

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