Question

(1+tan A)cot A / cosec? A = tan A​

Answer 1

Answer:

${ \sf{ \frac{1 + tan² \: A \: \times cot \: A}{cosec² \: A} = tan \: A}}$

${ \to{ \sf{ \frac{ {sec }^{2} A\times cot \: A}{ {cosec}^{2} \: A} = tan \: A}}}$

${ \boxed{ \to{ \sf{ {sec}^{2} A = \frac{1}{ {cos}^{2} A } }}}}$

${ \boxed{ \to{ \sf{ cot \: A \: = \frac{cos \: A}{sin \: A} }}}}$

${ \boxed{ \to{ \sf{ {cosec}^{2} A = \frac{1}{ {sin}^{2} A} }}}}$

${ \to{ \sf{ \frac{ \frac{1}{ {cos}^{2} \: A} \times \frac{cos \: A}{sin \: A} }{ \frac{1}{ {sin}^{2} A} } }}}$

${ \to{ \sf{ \frac{ {sin}^{2} A}{sin \: A \: \times cos \: A} }}}$

${ \to{ \sf{ \frac{sin \: A}{cos \: A} }}}$

${ \to{ \sf{tan \: A}}}$

${ \therefore{ \sf{ \frac{1 + {tan}^{2} A\times cot \: A}{ {cosec}^{2} A} = tan \: A}}}$