Question

If cos x = |sin x| then, the general solution is

• A. $x = n \pi + (-1)^n \frac{\pi}{4} , n \in Z $
• B. $x = n \pi \pm \frac{\pi}{4} , n \in Z $
• C. $x = (2n - 1) \pi \pm \frac{\pi}{4} , n \in Z $
• D. $x = 2n \pi \pm \frac{\pi}{4} , n \in Z $

Answer 1

Answer: (D)

$cos\, x=\left|sin\, x\right|$
$\Rightarrow \, \pm cos x=sin x$
$\Rightarrow \, tan x=\pm1$
$x=n\pi \pm\frac{\pi}{4}, n\in Z, but \,cos\, x \,is\, positive\, so \,x\,=2n \pi\pm\frac{\pi}{4}, n\in Z.$