Question

$\pi <\theta <2\pi$, $x=\frac{1}{\sin \theta -\sqrt{{\cot }^2\theta -{\cos }^2\theta }}=$

• A. $cosec\theta$
• B. $\sec \theta$
• C. $\sin \theta$
• D. $\cos \theta$

Answer 1

Answer: (C)

$\sin \theta$

$x=\frac{1}{\sin \theta -\sqrt{{\cot }^2\theta -{\cos }^2\theta }}$
Resolve: $\cot \theta =\frac{\cos \theta }{\sin \theta }$
$=\frac{1}{\sin \theta -\sqrt{{\cos }^2\theta {\cot }^2\theta }}$
$=\frac{1}{\sin \theta -|\cos \theta \cot \theta |}$
$=\frac{1}{\sin \theta +\cos \theta \cot \theta }$
$=\sin \theta$