Question

How do you simplify $\frac{\tan \left(x\right)}{sec\left(x\right)}$?

Answer 1

Simplify using the trigonometric identities.

We have to simplify $\frac{\tan \left(x\right)}{sec\left(x\right)}$

We will express $secx$ and$\tan x$ in terms of$\sin$and $\cos$.

$$\begin{gathered} \Rightarrow \frac{\tan x}{secx}=\frac{{\displaystyle \frac{\sin x}{\cos x}}}{{\displaystyle \frac{1}{\cos x}}} \\ \Rightarrow \frac{\tan x}{secx}=\frac{\sin x}{\cos x}\times \frac{1}{\cos x} \\ \Rightarrow \frac{\tan x}{secx}=\sin x \end{gathered}$$

Hence, the required answer is $\frac{\tan x}{secx}=\sin x$