Question

Prove that $(cosecA-\cot A{)}^2=\frac{(1-\cos A)}{(1+\cos A)}$.

Answer 1

Now,

$(cosecA-\cot A{)}^2$

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

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

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

$=\frac{(1-\cos A)}{(1+\cos A)}$.