The function \[f(x)={{\tan }^{-1}}(\sin x+\cos x)\], \[x>0\] is always an increasing function on the interval [Kerala (Engg.) 2005]

The function \[f(x)={{\tan }^{-1}}(\sin x+\cos x)\], \[x>0\] is always

1.	The function \[f(x)={{\tan }^{-1}}(\sin x+\cos x)\], \[x>0\] is always an increasing function on the interval [Kerala (Engg.) 2005]
A.	\[(0,\,\pi )\]
B.	\[(0,\,\pi /2)\]
C.	\[(0,\pi /4)\]
D.	\[(0,\,3\pi /4)\]
E.	\[(0,\,5\pi /4)\]
Answer» D. \[(0,\,3\pi /4)\]

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The function \[f(x)={{\tan }^{-1}}(\sin x+\cos x)\], \[x>0\] is always an increasing function on the interval [Kerala (Engg.) 2005]

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