Question

The value of (1 - cosec^2 A) tan^2 A is :​

Answer 1

$(1 - {cosec}^{2} a) {tan}^{2} a \\ = ( - {cot}^{2} a) {tan}^{2} a \\ = - \frac{1}{ {tan}^{2} a} {tan}^{2} a \\ = - 1$

Answer 2

$(1 - {cosec}^{2} A) {tan}^{2} A$

$\implies \: ( - {cot}^{2} A)ta {n}^{2} A$

$\implies \: - \frac{1}{ {tan}^{2}A } \times {tan}^{2} A$

$\implies \: - 1$

Formulas used :

$1 + {cot}^{2}A = {cosec}^{2}A \\ \implies1 - {cosec}^{2} A = - {cot}^{2} A$

$Cot \: A = \frac{1}{tan \: A}$