Question : The value of $\left(\tan ^2 A+\cot ^2 A-2\right)-\sec ^2 A \operatorname{cosec}^2 A$ is:

Option 1: –4

Option 2: –1

Option 3: 1

Option 4: 4

Question : The value of $\frac{3\left(\operatorname{cosec}^2 26^{\circ}-\tan ^2 64^{\circ}\right)+\left(\cot ^2 42^{\circ}-\sec ^2 48^{\circ}\right)}{\cot \left(22^{\circ}-\theta\right)-\operatorname{cosec}^2\left(62^{\circ}+\theta\right)-\tan \left(\theta+68^{\circ}\right)+\tan ^2\left(28^{\circ}-\theta\right)}$ is:

Option 1: 3

Option 2: 4

Option 3: –1

Option 4: –2

Question : The value of $\sqrt{\frac{1+\cos A}{1-\cos A}}$ is:

Option 1: $\sec A – \tan A$

Option 2: $\operatorname{cosec} A + \cot A$

Option 3: $\sec A + \tan A$

Option 4: $\operatorname{cosec} A – \cot A$

Question : The value of $\frac{3\left(\cot ^2 47^{\circ}-\sec ^2 43^{\circ}\right)-2\left(\tan ^2 23^{\circ}-\operatorname{cosec}^2 67^{\circ}\right)}{\operatorname{cosec}^2\left(68^{\circ}+\theta\right)-\tan \left(\theta+61^{\circ}\right)-\tan ^2\left(22^{\circ}-\theta\right)+\cot \left(29^{\circ}-\theta\right)}$ is:

Option 1: –1

Option 2: 1

Option 3: 5

Option 4: 0

Question : $\left(\frac{\tan ^3 \theta}{\sec ^2 \theta}+\frac{\cot ^3 \theta}{\operatorname{cosec}^2 \theta}+2 \sin \theta \cos \theta\right) \div\left(1+\operatorname{cosec}^2 \theta+\tan ^2 \theta\right), 0^{\circ}<\theta<90^{\circ}$, is equal to:

Option 1: $\operatorname{cosec} \theta \sec \theta$

Option 2: $\operatorname{cosec} \theta$

Option 3: $\sin \theta \cos \theta$

Option 4: $\sec \theta$

Question : The value of $\sqrt{\frac{1+\cos \theta}{1-\cos \theta}}$ is:

Option 1: $\sec\theta+\tan \theta$

Option 2: $\operatorname{cosec} \theta-\cot \theta$

Option 3: $\operatorname{cosec} \theta+\cot \theta$

Option 4: $\sec\theta-\tan \theta$