Question

evaluate: cosec 13/ sec 77- cot 20/ tan 70

Answer 1

We have the following formula,

$\sec (90^o-\theta)=\csc \theta\\ \tan (90^o-\theta)=\cot \theta$

Using the above identities,

$\sec 77^o=\csc 13^o\\ \tan 70^o=\cot 20^o$

Therefore,

$\frac{\csc 13^o}{\sec 77^o}=1\\ \frac{\cot 20^o }{\tan 70^o}=1$

$\frac{\csc 13^o}{\sec 77^o}-\frac{\cot 20^o }{\tan 70^o}=1 -1=0$