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Question

Show that f(x)=tan1(sinx+cosx) is an increasing function in (0,π4).

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Solution

We have,

f(x)=tan1(sinx+cosx)

dfdx=11+(sinx+cosx)2(sinxcosx)

dfdx=cosxsinx1+(sinx+cosx)2

For x(0,π4),cosx>sinx

dfdx>0

f(x) increases in (0,π4).

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