The value of the limit $\mathop {\lim }\limits_{\theta \to 0} \frac{{\tan \,(\pi {{\cos }^2}\theta )}}{{\sin \,(2\pi {{\sin }^2}\theta )}}$ is equal to

JEE MATHEMATICS MCQ: LIMITS

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The value of the limit

\lim\limits_{\theta \to 0} \frac{{\tan \,(\pi {{\cos }^2}\theta )}}{{\sin \,(2\pi {{\sin }^2}\theta )}}

is equal to

View answer and explanation

Correct option: A

- \frac{1}{2}

Option A (-1/2) is correct. The limit can be evaluated using trigonometric identities and L'Hopital's rule or by converting to sine functions and using limit properties.

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