Question

prove that :
1-tan sq / cot sq -1 = tan sq​

Answer 1

Correct Question:-

$\frac{1 - {tan}^{2} \theta}{ {cot}^{2} \theta - 1} = {tan}^{2} \theta$

Solution :-

Taking LHS

$\implies\: \frac{1 - {tan}^{2} \theta }{ {cot}^{2} \theta - 1 } \\ \\ \implies \: \frac{1 - \frac{ {sin}^{2} \theta }{ {cos}^{2} \theta} }{ \frac{ {cos}^{2} \theta}{ {sin}^{2} \theta } - 1 } \\ \\ \implies \frac{ \frac{ {cos}^{2} \theta - {sin}^{2} \theta }{ {cos}^{2} \theta} }{ \frac{ {cos}^{2} \theta - {sin}^{2} \theta}{ {sin}^{2} \theta} } \\ \\ \implies \frac{ {cos}^{2} \theta - {sin}^{2} \theta }{ {cos}^{2} \theta} \times \frac{ {sin}^{2} \theta }{ {cos}^{2} \theta - {sin}^{2} \theta} \\ \\ \implies \frac{ {sin}^{2} \theta}{ {cos}^{2} \theta } \\ \\ \implies {tan}^{2} \theta = RHS$

${\purple{\boxed{\large{\bold{LHS=RHS}}}}}$

Proved