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Question

f(x)=tan1(sinx+cosx) is an increasing function in

A
(0,π4)
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B
(0,π2)
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C
(π4,π4)
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D
None of these
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Solution

The correct options are
B (0,π4)
D (π4,π4)
f(x)=tan1(sinx+cosx)
f1(x)=11+(sinx+cosx)2 (cosxsinx)
always positive g(x)
g(x)=cosxsinx
g(x)=0tanx=1 x=π4
[3π4,π4] increasing function
So, answers are (0,π4),(π4,π4)

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