Question : If $\theta$ be an acute angle and $\tan \theta+\cot \theta=2$, then the value of $2 \tan ^2 \theta+\cot ^2 \theta+\tan ^4 \theta \cot ^4 \theta$ is:

Option 1: 4

Option 2: 2

Option 3: 3

Option 4: 6

Question : $(\sin \theta+\operatorname{cosec} \theta)^2+(\cos \theta+\sec \theta)^2=$?

Option 1: $5+\tan ^2 \theta+\cot ^2 \theta$

Option 2: $7+\tan ^2 \theta-\cot ^2 \theta$

Option 3: $7+\tan ^2 \theta+\cot ^2 \theta$

Option 4: $5+\tan ^2 \theta-\cot ^2 \theta$

Question : $\tan(θ -14\pi)$ is equal to:

Option 1: $\tan \theta$

Option 2: $-\cot \theta$

Option 3: $\cot \theta$

Option 4: $-\tan \theta$

Question : A clock tower stands at the crossing of two roads which point in the north-south and the east-west directions. $P, Q, R$, and $S$ are points on the roads due north, east, south, and west respectively, where the angles of elevation of the top of the tower are respectively, $\alpha, \beta, \gamma$ and $\delta$. Then $\left(\frac{\mathrm{PQ}}{\mathrm{RS}}\right)^2$ is equal to:

Option 1: $\frac{\tan ^2 \alpha+\tan ^2 \beta}{\tan ^2 \gamma+\tan ^2 \delta}$

Option 2: $\frac{\cot ^2 \alpha+\cot ^2 \beta}{\cot ^2 \gamma+\cot ^2 \delta}$

Option 3: $\frac{\cot ^2 \alpha+\cot ^2 \delta}{\cot ^2 \beta+\cot ^2 \gamma}$

Option 4: $\frac{\tan ^2 \alpha+\tan ^2 \delta}{\tan ^2 \beta+\tan ^2 \gamma}$

Question : $\frac{\cos A}{1-\tan A}+\frac{\sin A}{1-\cot A}=$___________.

Option 1: $\tan A - \cot A$

Option 2: $\tan A + \cot A$

Option 3: $\sin A - \cos A$

Option 4: $\sin A + \cos A$