Question

The expression $\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}$ can be written as

• A. $\sin A\cos A+1$
• B. $\sec A\csc A+1$
• C. $\tan A+\cot A$
• D. $\sec A+\csc A$

Answer 1

The correct option is B $\sec A\csc A+1$

$\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}$

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

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

$=\sec A\csc A+1$