Question : $2\ \text{cosec}^{2}\: 23°\cot^{2}67°-\sin^{2}23°-\sin^{2}67°-\cot^{2}67°$ is equal to:

Option 1: $1$

Option 2: $\sec^{2}23°$

Option 3: $\tan^{2}23°$

Option 4: $0$

Question : The value of $\frac{\sec 54^{\circ}}{\operatorname{cosec} 36^{\circ}}+\frac{\tan 70^{\circ}}{\cot 20^{\circ}}-2 \tan 45^{\circ}$ is equal to:

Option 1: 2

Option 2: 0

Option 3: 1

Option 4: 3

Question : What is the value of $\frac{1+\tan A}{\operatorname{cosec} A}+\frac{1+\cot A}{\sec A}$?

Option 1: $2\sec^2A$

Option 2: $\sec \mathrm{A} - \mathrm{cosec A}$

Option 3: $\sec \mathrm{A} + \mathrm{cosec A}$

Option 4: $2 \;\mathrm{cosec^2 A}$

Question : What is the value of $\frac{3 \operatorname{cosec} 42°}{\sec 48°}-\frac{5 \cos 32°}{\sin 58°}$?

Option 1: - 1

Option 2: 5

Option 3: 0

Option 4: - 2

Question : If $\alpha +\beta =90^{\circ}$, then the expression $\frac{\tan \alpha}{\tan \beta}+\sin^{2}\alpha+\sin^{2}\beta$ is equal to:

Option 1: $\sec^{2}\beta$

Option 2: $\tan^{2}\alpha$

Option 3: $\tan^{2}\beta$

Option 4: $\sec^{2}\alpha$

Question : Simplify the given expression.
$\sqrt{\frac{1+\cos P}{1-\cos P}}$

Option 1: $\operatorname{cosec}P-\cot P$

Option 2: $\sec P-\tan P$

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

Option 4: $\operatorname{cosec} P+\cot P$