Question

If $A$ and $B$ are complemetary angles, then $\sqrt{\frac{\cos A}{\sin B}}-\cos A\sin B=$

• A. $\cos A\sin A$
• B. ${\cos }^{2}A$
• C. ${\sin }^{2}A$
• D. ${\sin }^{2}B$

Answer 1

The correct option is C ${\sin }^{2}A$

As $A$ and $B$ are complemetary angles, so
$A+B=\frac{\pi }{2}$

Now,
$\sqrt{\frac{\cos A}{\sin B}}-\cos A\sin B=\sqrt{\frac{\cos A}{\sin (\frac{\pi }{2}-A)}}-\cos A\sin (\frac{\pi }{2}-A)=\sqrt{\frac{\cos A}{\cos A}}-\cos A\cos A=1-{\cos }^{2}A={\sin }^{2}A={\cos }^{2}B$