Question : The value of $23\operatorname{cosec}^2 A-23\cot^2A$ is:

Option 1: 23

Option 2: 1

Option 3: 27

Option 4: 0

Question : The value of $\frac{\sin A}{\cot A+\operatorname{cosec} A}-\frac{\sin A}{\cot A-\operatorname{cosec} A}+1$ is:

Option 1: $\frac{1}{2}$

Option 2: $3$

Option 3: $0$

Option 4: $2$

Question : If the value of $\operatorname{cosec} A + \cot A = m$, then the value of $\operatorname{cosec} A - \cot A$ is:

Option 1: $\frac{1}m$

Option 2: $m$

Option 3: $\sqrt{m}$

Option 4: $m^2$

Question : The value of $\sqrt{\frac{1+\sin A}{1-\sin A}}$ 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 $\tan ^2 48^{\circ}-\operatorname{cosec}^2 42^{\circ}+\operatorname{cosec}\left(67^{\circ}+\theta\right)-\sec \left(23^{\circ}-\theta\right)$ is:

Option 1: $-1$

Option 2: $0$

Option 3: $1$

Option 4: $-2$

Question : The value of $(\operatorname{cosec}A+\cot A)(1 - \cos A)$ is:

Option 1: $\cos A$

Option 2: $\tan A$

Option 3: $\cot A$

Option 4: $\sin A$