Question

The values of $x$ which satisfying both the equations $\cos x=\frac{-1}{\sqrt{2}}$ and $\tan x=1$ simultaneously is :

• A. $n\pi +\frac{5\pi }{4},n\in Z$
• B. $2n\pi +\frac{5\pi }{4},n\in Z$
• C. $n\pi -\frac{5\pi }{4},n\in Z$
• D. $2n\pi +\frac{\pi }{4},n\in Z$

Answer 1

The correct option is B $2n\pi +\frac{5\pi }{4},n\in Z$

$\cos x=\frac{-1}{\sqrt{2}}\Rightarrow x=\frac{3\pi }{4},\frac{5\pi }{4}$
and $\tan x=1$
$\Rightarrow x=\frac{\pi }{4},\frac{5\pi }{4}$
$\Rightarrow$ Common solution $=\frac{5\pi }{4}$
General solution $=2n\pi +\frac{5\pi }{4},n\in Z$