Question : The value of the expression $\left (1+\sec22^{\circ} +\cot68^{\circ} \right )\left (1-cosec\;22 ^{\circ} +\tan68^{\circ} \right )$ is:

Option 1: 0

Option 2: 1

Option 3: –1

Option 4: 2

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

Option 1: –1

Option 2: 1

Option 3: 5

Option 4: 0

Question : The value of $\frac{\left(\cos 9^{\circ}+\sin 81^{\circ}\right)\left(\sec 9^{\circ}+{\operatorname{cosec}} \;81^{\circ}\right)}{{\operatorname{cosec}}^2 \;71^{\circ}+\cos ^2 15^{\circ}-\tan ^2 19^{\circ}+\cos ^2 75^{\circ}} $ is:

Option 1: 1

Option 2: 4

Option 3: 5

Option 4: 2

Question : If $\sin\left ( 2a+45^{\circ} \right )=\cos\left ( 30^{\circ}-a \right )$ where $0^{\circ}< a< 90^{\circ}$, then the value of a is:

Option 1: $0^{\circ}$

Option 2: $15^{\circ}$

Option 3: $45^{\circ}$

Option 4: $60^{\circ}$

Question : Find the value of $\cos 47^\circ \sec 133^\circ + \sin 44^\circ \text{cosec}\; 136^\circ $.

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

Option 2: $1$

Option 3: $0$

Option 4: $–1$