Question

Which of the following is equivalent to $\frac{\tan n\text{cosec}n}{\sin n\sec n}$?

• A. $1$
• B. $\sin n$
• C. $\cos n$
• D. $\cot n$
• E. $\text{cosec}n$

Answer 1

The correct option is E $\text{cosec}n$

We know that $\tan n=\frac{\sin n}{\cos n}$

$\text{cosec}n=\frac{1}{\sin n}$

$\sec n=\frac{1}{\cos n}$

Thus, $\frac{\tan n\text{cosec}n}{\sin n\sec n}=\frac{\frac{\sin n}{\cos n}\times \frac{1}{\sin n}}{\sin n\times \frac{1}{\cos n}}=\frac{1}{\sin n}=\text{cosec}n$