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The function f(x)=tan^(-1)(sinx+cosx) is...

The function `f(x)=tan^(-1)(sinx+cosx)` is an increasing function in `(-pi/2,pi/4)` (b) `(0,pi/2)` `(-pi/2,pi/2)` (d) `(pi/4,pi/2)`

A

`(0,pi//2)`

B

`(0,(pi)/(2))`

C

`(-(pi)/(2),(pi)/(2))`

D

`((pi)/(4),(pi)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
1
Here fX() =`tan^(-1) (sinx+cosx)`
`therefore f(X)=(1)/(1+(sinx+cosx)^(2)(cosx-sinx)`
`=(cosx-sinx)/(2+sin 2 x)`
`for -(pi)/(2)ltxlt(pi)/(4),cos x gtsinx`
Hence y = f(X) is increasing in `(-(pi)/(2),(pi)/(4))`
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Show that f(x)=tan^(-1)(sinx+cosx) is a decreasing function on the interval on (pi//4,\ pi//2) .

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