Question

EVALUATE

TAN36°/cos54°​

Answer 1

$\huge \bold{ \mathtt{ \frac{tan {36}^{0} }{cos {54}^{0} } }}$

$\large = \frac{tan( {90}^{0} - {54}^{0}) }{cos {54}^{0} }$

$\large = \frac{cot \: {54}^{0} }{cos \: {54}^{0} }$

$\large= \frac{ \frac{cos \: {54}^{0} }{sin \: {54}^{0} } }{cos \: {54}^{0} }$

$\large = \frac{cos \: {54}^{0} }{sin \: {54}^{0} } \times \frac{1}{cos \: {54}^{0} }$

$\large= \frac{1}{sin {54}^{0} }$

$= \bold{ \boxed{ \mathtt { \color{blue}{cosec \: {54}^{0} }}}}$

Trigonometric Identity used:—

$\Large\bold{ \boxed{ \mathtt{ \color{red}{tan \: ( {90}^{0} - \theta) = \: cot \theta }}}}$