Question

If $x+y={90}^{\circ }$, then what is $\sqrt{\cos x\text{cosec}y-\cos x\sin y}$ equal to?

• A. $\cos x$
• B. $\sin x$
• C. $\sqrt{\cos x}$
• D. $\sqrt{\sin x}$

Answer 1

The correct option is B $\sin x$

$\sqrt{\cos x\text{cosec}(90-x)-\cos x.\sin (90-x)}$
$=\sqrt{\cos x.\sec x-\cos x.\cos x}$
$=\sqrt{1-{\cos }^{2}x}=\sqrt{{\sin }^{2}x}=\sin x$