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

Question

The function f(x) = tan-1 (sin x + cos x) is an increasing function in (A) ((π/4), (π/2)) (B) (-(π/2), (π/4)) (C) (0, (π/2)) (D) (-(π/2), (π/2))

Tardigrade Admin · Accepted Answer

f'(x) = (1/1+(sin x + cos x)2) (cos x - sin x) f(x) is increasing if cos x - sin x > 0 or cos x > sin x Hence, f(x) is increasing when x∈(-(π/2), (π/4))

Q. The function $f (x) = t a n^{- 1} (s in x + cos x)$ is an increasing function in

$(\frac{π}{4}, \frac{π}{2})$

$(- \frac{π}{2}, \frac{π}{4})$

$(0, \frac{π}{2})$

$(- \frac{π}{2}, \frac{π}{2})$

$f^{'} (x) = \frac{1}{1 + ( s in x + cos x ) ^{2}} (cos x - s in x)$
$f (x)$ is increasing if
$cos x - s in x > 0$
or $cos x > s in x$
Hence, $f (x)$ is increasing when
$x \in (- \frac{π}{2}, \frac{π}{4})$

Q. The function f(x)=tan−1(sinx+cosx) is an increasing function in

(4π​,2π​)

(−2π​,4π​)

(0,2π​)

(−2π​,2π​)