Question

# Find the value of $\theta$ If $\sec \theta .\sin \theta = 0$ .

Hint: Here, we will use trigonometric formulae of $\sec \theta$ to simplify the equation and then using the properties of trigonometry the value of can be computed.
$\sec \theta .\sin \theta = 0 \to (1)$
As, we know that $\sec \theta = \dfrac{1}{{\cos \theta }}$, let us substitute in equation (1) we get
$\Rightarrow \dfrac{1}{{\cos \theta }}(\sin \theta ) = 0 \\ \Rightarrow \tan \theta = 0 \\ \Rightarrow \tan \theta = \tan (n\pi ) \to (2) \\$
The $'\tan '$ on the both sides of equation (2) gets cancelled and we get the value of $\theta$ i.e..,
$\theta = n\pi$
Hence, the value of $\theta$ is $n\pi$
Note: The value of $\tan (n\pi )$ is always 0, since $\sin (n\pi ) = 0$ , where n is an integer number.