Question

$\underset{\theta \to \pi /2}{lim}\frac{1-\sin \theta }{(\pi /2-\theta )\cos \theta }$ is equal to

Answer 1

We have,

${lim}_{\theta \to \frac{\pi }{2}}\frac{1-\sin \theta }{(\frac{\pi }{2}-\theta )\cos \theta }\left(\frac{0}{0}form\right)$

Applying L’ Hospital rule and we get,

${lim}_{\theta \to \frac{\pi }{2}}\frac{0-\cos \theta }{(\frac{\pi }{2}-\theta )(-\sin \theta )+\cos \theta (0-1)}$

Taking limit and we get,

$\Rightarrow \frac{-\cos \frac{\pi }{2}}{(\frac{\pi }{2}-\frac{\pi }{2})(-\sin \frac{\pi }{2})-\cos \frac{\pi }{2}}$

$\Rightarrow 0$

Hence, this is the answer.