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Geometry Level 3

If $\cot \theta \ \sqrt{1 - \cos^2\theta} = 1$ and $\theta = [0^\circ,360^\circ)$

Find the solution set of $\theta$ .

x = {0} x = {90,270} x = {90} x = {0,180} None of the choices x = {180} x={270}

1 solution

Paul Ryan Longhas
Apr 29, 2015

Since, $\cot \theta \sqrt{1-\cos^2\theta} = 1 \Rightarrow \cot \theta|\sin\theta| = 1$

$\Rightarrow \cos \theta = 1$ or $\cos \theta = -1$

So, $\sin \theta = 0$

But if $\sin \theta = 0 \Rightarrow \cot\theta$ is undefined.

So, the answer is "None of the choices".

Arghhhhh! you got me!Nice problem

Arian Tashakkor - 6 years, 1 month ago

This problem reminded me to remember the basics :)

Aditya Garg - 6 years, 1 month ago

Ah! JEE standards !!

Abhishek Singh - 6 years ago