Question

Evaluate the following :$\frac{\cos {55}^o\csc {35}^o}{\tan 5^o\tan {25}^o\tan {65}^o\tan {85}^o}$

Answer 1

$\to$ Assuming $csc35=cosec35$

As $coses35=\frac{1}{\sin 35}=\frac{1}{\sin (90-55)}$

and $\sin (90-\theta )=cos\theta$

$\Rightarrow coses35=(\cos 55{)}^{-1}$

Similarly $tan85=\frac{1}{\cot 85}=\frac{1}{\tan 5}$

and $\tan 65=\frac{1}{\cot 65}=\frac{1}{\tan 25}$

So Quantity $=\frac{1}{1\times 1}=1$