Question

Fundamental period of the function $f\left(x\right)=\frac{(1+\sin x)(1+\sec x)}{(1+\cos x)(1+\text{cosec}x)},x\in R-\left\{\right(2n+1)\pi ,\frac{(4m-1)\pi }{2},n,m\in Z\}$ is

• A. $\frac{\pi }{2}$
• B. $\pi$
• C. $2\pi$
• D. $1$

Answer 1

The correct option is B $\pi$

$f\left(x\right)=\frac{(1+\sin x)(1+\sec x)}{(1+\cos x)(1+\text{cosec}x)}$
$=\frac{(1+\sin x)(1+\frac{1}{\cos x})}{(1+\cos x)(1+\frac{1}{\sin x})}$
$=\frac{\sin x}{\cos x}=\tan x$
Hence, fundamental period of $f\left(x\right)$ is $\pi .$