Question

$\frac{\cos A}{1-\tan A}+\frac{\sin A}{1-\cot A}$is equal to

• A. $\sin A-\cos A$
• B. $\sin A+\cos A$
• C. $1-\cos A$
• D. $1-\sin A$

Answer 1

Answer: (B)

$\sin A+\cos A$

Simplifying the above equation we get

$\frac{\cos A}{1-\tan A}+\frac{\sin A}{1-cotA}$

$=\frac{\cos A}{1-\frac{\sin A}{\cos A}}+\frac{\sin A}{1-\frac{\cos A}{\sin A}}$

$=\frac{{\cos }^{2}A}{\cos A-\sin A}+\frac{{\sin }^{2}A}{\sin A-\cos A}$

$=\frac{{\cos }^{2}A-{\sin }^{2}A}{\cos A-\sin A}$

$=\frac{(\cos A-\sin A)(\cos A+\sin A)}{\cos A-\sin A}$

$=\cos A+\sin A$

Hence answer is B