Q.

The function f(x)=tan-1(sinx+cosx) is an  increasing function in

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a

0,π2

b

-π2,π2

c

π4,π2

d

-π2,π4

answer is D.

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Detailed Solution

Given fx=tan−1sinx+cosxDifferentiate both sides with respect to xf'x=11+sinx+cosx2cosx−sinx=21+sinx+cosx212cosx−12sinx=21+sinx+cosx2cosπ4cosx−sinπ4sinx=2cosx+π41+sinx+cosx2If f'x>0 then fx is increasing function hence fx is increasing if −π2
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The function f(x)=tan-1(sinx+cosx) is an  increasing function in