If $x = \sec \theta + \tan \theta ,$ then $x + \frac{1}{x} = $

Prove that $\frac{\cos (\pi+x) \cos (-x)}{\sin (\pi-x) \cos (\frac{\pi}{2}+x)} = \cot^{2} x$.

The expression $\frac{\tan \left( \frac{3\pi}{2} - \alpha \right) \cos \left( \frac{3\pi}{2} - \alpha \right)}{\cos (2\pi - \alpha )} + \cos \left( \alpha - \frac{\pi}{2} \right) \sin (\pi - \alpha ) + \cos (\pi + \alpha ) \sin \left( \alpha - \frac{\pi}{2} \right)$ when simplified reduces to:

If $\operatorname{cosec} \theta + \cot \theta = \frac{1}{3}$,then $\theta$ lies in the

If $\cot \theta = -\frac{2}{3}$ and $\theta$ does not lie in the $4^{\text{th}}$ quadrant,then $\frac{(5 \sin \theta + \cos \theta)^2}{\tan \theta + \cot \theta} = $

Which of the following statements is incorrect?