Question : The value of $(1+\sec20°+\cot70°)(1-\operatorname{cosec}20°+\tan70°)$ is equal to:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: –1

Question : If $\operatorname{cosec} \theta + \operatorname{cot} \theta = m$, find the value of$\frac{m^2 – 1}{m^2 + 1}$

Option 1: $1$

Option 2: $0$

Option 3: $\operatorname{cos} \theta$

Option 4: $\operatorname{–sin} \theta$

Question : The value of $\tan315°.\cot(-405°)$, is equal to:

Option 1: –1

Option 2: 1

Option 3: 0

Option 4: 2

Question : The value of $\operatorname{cosec}^{2}60°+\sec^{2}60°– \cot^{2}60°+\tan^{2}30°$ will be:

Option 1: $5$

Option 2: $5\frac{1}{2}$

Option 3: $5\frac{1}{3}$

Option 4: $5\frac{2}{3}$

Question : If $\sec 2 \theta=\operatorname{cosec}(\theta-36°)$, where $2 \theta$ is an acute angle, find the value of $\theta$.

Option 1: 32°

Option 2: 46°

Option 3: 20°

Option 4: 42°

Question : If $\sin\theta+\operatorname{cosec}\theta=2$, the value of $\sin^{n}\theta+\operatorname{cosec}^{n}\theta$ is:

Option 1: $2^{n}$

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

Option 3: $2$

Option 4: $0$