Question

$(cotA-cosecA{)}^2=\frac{1-cosA}{1+cosA}$

Answer 1

RHS = $\frac{1-cosA}{1+cosA}\times \frac{1-cosA}{1-cosA}$

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

$=\frac{(co{s}^{2}A-1{)}^2}{si{n}^{2}A}$

LHS $=(cotA-cosecA{)}^2$

$=(\frac{cosA}{sinA}-\frac{1}{sinA}{)}^2$

$\frac{(cosA-1{)}^2}{si{n}^{2}A}$

= RHS

$\therefore$ Hence, proved