Question

Evaluate:

$\frac{\tan {50}^o+\sec {50}^o}{\cot {40}^o+\csc {40}^o}+{cos40}^o.{csc50}^o$ = ?

Answer 1

$\frac{\tan {50}^{\circ }+\sec {50}^{\circ }}{\cot {40}^{\circ }+\csc {40}^{\circ }}+\cos {40}^{\circ }\csc {50}^{\circ }\frac{\frac{\sin {50}^{\circ }}{\cos {50}^{\circ }}+\frac{1}{\cos {50}^{\circ }}}{\frac{\cos {40}^{\circ }}{\sin {40}^{\circ }}+\frac{1}{\sin {40}^{\circ }}}+\cos {40}^{\circ }\frac{1}{\sin {50}^{\circ }}\frac{\frac{1+\sin {50}^{\circ }}{\cos {50}^{\circ }}}{\frac{1+\cos {40}^{\circ }}{\sin {40}^{\circ }}}+\frac{\cos {40}^{\circ }}{\cos {40}^{\circ }}\frac{\frac{1+\cos {40}^{\circ }}{\cos {50}^{\circ }}}{\frac{1+\cos {40}^{\circ }}{\cos {50}^{\circ }}}+11+1=2$