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The function f (x) = tan–1(sin x + cos x) is an increasing function in ?

The function f (x) = tan–1(sin x + cos x) is an increasing function in ?

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
f(x) = tan^{-1}(sinx + cosx)
f^{'}(x) = \frac{cosx - sinx}{1 + (sinx+cosx)^{2}}> 0
cosx> sinx
tanx <1
In the interval
(0, 2\pi )
x belongs to
0< x<\frac{\pi }{4}
\frac{\pi }{2}< x<\frac{5\pi }{4}
\frac{3\pi }{2}< x<2\pi
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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