The function fx=tan-1sinx+cosx is an increasing function on the interval
0,π
0,π2
0,π4
0,3π4
0,5π4
Find the interval in which the given function is increasing
We know that a function fx is increasing then f'x>0
fx=tan-1sinx+cosx⇒y=tan-12sinx+π4Lety=f(x)⇒tany=2sinx+π4⇒sec2ydydx=-2cosx+π4
So,
=dydx>0=cosx+π4>0=x∈0,π4
Hence option C is correct.