Which of the following is correct?

If $\tan \theta + \cot \theta = 5,$ then $\tan^2 \theta + \cot^2 \theta$ is

If $\cos \theta = \frac{8}{17}$ and $\theta$ lies in the $1^{st}$ quadrant,then the value of $\cos (30^\circ + \theta) + \cos (45^\circ - \theta) + \cos (120^\circ - \theta)$ is

The angle of elevation of the top of an unfinished tower at a point $120\, m$ from its base is $45^{\circ}$. How much higher must the tower be raised so that its angle of elevation at the same point be $60^{\circ}$? (in $m$)

Without using trigonometric tables,evaluate: $\sin 48^{\circ} \sec 42^{\circ} + \cos 48^{\circ} \operatorname{cosec} 42^{\circ} = $

If $\sin \theta_1 + \sin \theta_2 + \sin \theta_3 = 3,$ then $\cos \theta_1 + \cos \theta_2 + \cos \theta_3 =$