Let f(x)= (x-a)+ (x+a) (x-a)- (x+a) , then - Vidyadip

MCQ

Let $f(x)=\frac{\sin (x-a)+\sin (x+a)}{\cos (x-a)-\cos (x+a)}$, then

A
$f(x+2 \pi)=f(x)$ but $f(x+\alpha) \neq f(x)$ for any $0<\alpha < 2 \pi$
B
$f$ is a strictly increasing function
C
$f$ is a strictly decreasing function
✓
$f$ is a constant function

✓

Answer

Correct option: D.

$f$ is a constant function

d
(d)

We have,

$f(x)=\frac{\sin (x-a)+\sin (x+a)}{\cos (x-a)-\cos (x+a)}$

$f(x)=\frac{2 \sin x \cos a}{2 \sin x \sin a}$

$f(x)=\cot a$

$\therefore f$ is constant function.

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