Question

$\frac{si{n}^3\theta -co{s}^3\theta }{sin\theta -cos\theta }-\frac{\cos \theta }{\sqrt{1+co{t}^2\theta }}-2tan\theta cot\theta =-1$ if:

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

note: $\sin \theta \ne \cos \theta$
$\Rightarrow \theta \notin \left(0,\frac{\pi }{2}\right)\cup \left(\pi ,\frac{3\pi }{2}\right);\theta \ne \frac{\pi }{2},\frac{3\pi }{2},0,\pi ,2\pi$
And equality holds if $\theta \in \left(\frac{\pi }{2},\pi \right)$