Question

Solve:

$\left(\frac{sinA}{1-cosA}\right)-\left(\frac{1-cosA}{sinA}\right)$=

• A. $2tanA$
• B. $2cotA$
• C. $2cot\frac{A}{2}$
• D. $2tan\frac{A}{2}$

Answer 1

The correct option is B $2cotA$

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

$=\frac{{\sin }^{2}A-{(1-\cos A)}^2}{\sin A(1-\cos A)}$

$=\frac{{\sin }^{2}A-1-{\cos }^{2}A+2\cos A}{\sin A(1-\cos A)}$

$=\frac{{\sin }^{2}A-{\cos }^{2}A-1+2\cos A}{\sin A(1-\cos A)}$

$=\frac{1-{\cos }^{2}A-{\cos }^{2}A-1+2\cos A}{\sin A(1-\cos A)}$

$=\frac{-2{\cos }^{2}A+2\cos A}{\sin A(1-\cos A)}$

$=\frac{2\cos A(1-\cos A)}{\sin A(1-\cos A)}$

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

$=2\cot A$