Question

If $\frac{\sin x}{1+\sec x}+\frac{\sin x}{\sec x-1}=2$ where $0^{\circ }<x<{90}^{\circ }$ then cosec x has the value equal to

• A. 1
• B. 2
• C. $\sqrt{2}$
• D. $\sqrt{3}$

Answer 1

The correct option is C $\sqrt{2}$

Given: $\frac{\sin x}{1+\sec x}+\frac{\sin x}{\sec x-1}=2$
$\frac{\sin x\sec x-\sin x+sinx+\sin xsecx}{(1+\sec x)(1-\sec x)}=2$
$\frac{2\sin x\sec x}{1-{\sec }^{2}x}=2$
$\frac{2\tan x}{{\tan }^{2}x}=2$
$\frac{2}{\tan x}=2$
$\tan x=1$
$\tan x=\tan 45$
$x={45}^{\circ }$
Thus, $cosecx=cosec45=\sqrt{2}$