Courses
Courses for Kids
Free study material
Offline Centres
More
Last updated date: 25th Nov 2023
Total views: 381.9k
Views today: 3.81k
MVSAT Dec 2023

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

Answer
VerifiedVerified
381.9k+ views
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.
Given,
$\sec \theta .\sin \theta = 0 \to (1)$
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.