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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. `((pi)/(2),(pi)/(2))`B. `(-(pi)/(2),(pi)/(4))`C. `(0,(pi)/(2))`D. `(-(pi)/(2),(pi)/(2))` |
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Answer» Correct Answer - B Since `f(x) = tan ^(-1) (sin x + cos x)` `rArr " " f(x) = (1)/(1+(sin x+ cos x)^(2)( cos x - sin x))` ` = (sqrt(2) cos(x+(pi)/(4)))/(1+(sin x+ cos x)^(2))` For f(x) to be increasing , `-(pi)/(2) lt x +(pi)/(4) lt (pi)/(2)` `rArr -(3pi)/(4) lt x lt (pi)/(4)` Hence , option (b) is correct , which lies in the above interal . |
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