If $z=\frac{1}{1-\cos \theta+i \sin \theta}$ and $\theta$ is acute then the modulus and amplitude of $z$…

If $z=\frac{1}{1-\cos \theta+i \sin \theta}$ and $\theta$ is acute then the modulus and amplitude of $z$ respectively are $$
  1. $\frac{1}{2} \operatorname{cosec} \frac{\theta}{2},-\left(\frac{\pi}{2}+\frac{\theta}{2}\right)$
  2. $\frac{1}{2} \operatorname{cosec} \frac{\theta}{2},\left(\frac{\pi}{2}+\frac{\theta}{2}\right)$
  3. $\frac{1}{2} \sec \frac{\theta}{2},-\left(\frac{\pi}{2}+\frac{\theta}{2}\right)$
  4. $\frac{1}{2} \sec \frac{\theta}{2},\left(\frac{\pi}{2}+\frac{\theta}{2}\right)$

Solution

No solution. Refer to answer key.

Asked in: AP EAMCET 2018 (24 Apr Shift 2)

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