Question

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

• A. $\sec A\text{cosec}A+1$
• B. $\tan A+\cot A$
• C. $\sec A+\text{cosec}A$
• D. $\sin A\cos A+1$

Answer 1

Answer: (A)

$\sec A\text{cosec}A+1$

$\frac{tanA}{1-cotA}+\frac{cotA}{1-tanA}$
$=\frac{1}{cotA(1-cotA)}-\frac{co{t}^{2}A}{1-\cot A}$
$=\frac{1-{\cot }^{3}A}{\cot A(1-\cot A)}$
$=\frac{\cos e{c}^{2}A+\cot A}{\cot A}$
$=1+secAcosecA$