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Question

If sin1xcos1x dx=f1(x)[Axxf1(x)21x2]+π21x2+2x+c, then


Correct Answer
A
f(x)=sinx
Your Answer
B
f(x)=cosx
Your Answer
C
A=π4
Correct Answer
D
A=π2

Solution

The correct options are
A f(x)=sinx
D A=π2
sin1xcos1xdx=[π2sin1xsin1x)2]dx

Integrating by parts
=π2(xsin1x+1x2)(x(sin1x)2+sin1x1x2x)+c 
=sin1x[π2xx sin1x21x2]+π21x2+2x+c

f1(x)=sin1x, A=π2
f(x)=sinx

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