$\text{Establish }\frac{\sin t}{1-\cos t}=\csc t+\cot t$

$\text{Establish }\frac{1}{\sin \alpha +\cos \alpha }=\frac{\tan \alpha +\cot \alpha }{\sec \alpha +\operatorname{cosec}\alpha }$

$\text{Establish that }\frac{{{\tan }^{2}}\theta +{{\cos }^{2}}\theta }{\sec \theta +\sin \theta }=\sec \theta -\sin \theta$

$\text{Establish that }\frac{1-\sin \theta +\cos \theta }{1-\sin \theta }=\frac{1+\sin \theta +\cos \theta }{\cos \theta }$

$\text{Establish that }\frac{\tan u-\tan v}{1+\tan u\tan v}=\frac{\cot v-\cot u}{1+\cot u\cot v}$

$\text{Find the values in terms of }p\text{ and }q\text{ of }\frac{p\cos \theta +q\sin \theta }{p\cos \theta -q\sin \theta }\text{ where }\cot \theta =\frac{p}{q}$

$\begin{align}  & \text{if }\cos \theta =\tfrac{4}{5}\text{ (i) }\sin \theta \text{ (ii) }\operatorname{cosec}\theta \text{  (iii) }\theta  \\ & \text{If }\sin \theta =-\tfrac{12}{13}\text{ (i) cos}\theta \text{ (ii) }\tan \theta  \\\end{align}$ 

$\begin{align}  & \text{Write down the general solution of the trigonometric equations} \\ & \cos (2\theta -{{30}^{\circ }})=0 \\\end{align}$

$\begin{align}  & \text{Write down the general solution of the trigonometric equations} \\ & 2\sin 2\theta +1=0 \\\end{align}$

$\text{Verify }\cos \left( \theta +\frac{\pi }{4} \right)=\frac{\sqrt{2}}{2}(\cos \theta -\sin \theta )$ 

$\text{Verify }\cot \left( t-\frac{\pi }{3} \right)=\frac{\sqrt{3}(\tan t+3)}{\tan t-\sqrt{3}}$

$\begin{align}  & \text{Obtain the first general solution of the  equation and then use the general } \\ & \text{solution to find all solution in the range }{{0}^{\circ }}\le \theta \le {{360}^{\circ }} \\ & 8{{\sin }^{2}}\theta -6\cos \theta =3 \\\end{align}$

$\begin{align}  & \text{Obtain the first general solution of the  equation and then use the general } \\ & \text{solution to find all solution in the range }{{0}^{\circ }}\le \theta \le {{360}^{\circ }} \\ & 3\sin 3\theta -\operatorname{cosec}3\theta +2=0 \\\end{align}$