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

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Last updated date: 19th Jul 2024
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Answer
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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.