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Question

sin1(cos(sin1x))+cos1(sin(cos1x))= ___________.

A
π2
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B
π4
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C
0
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D
π2
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Solution

The correct option is A π2
cos1x=sin11x2
sin(cos1x)=sin(sin11x2)=1x2

Similarly, cos(sin1x)=cos(cos11x2)=1x2

sin1(cos(sin1x))+cos1(sin(cos1x))

=sin1(1x2)+cos1(1x2)

=π2 ....[sin1(θ)+cos1(θ)=π2]

Hence, the answer is option (A).


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