Question : If $\sec^2 \theta+\tan^2 \theta=\frac{25}{18}$, the value of $\sec^4 \theta-\tan^4 \theta$ is:

Option 1: $\frac{18}{25}$

Option 2: $\frac{25}{12}$

Option 3: $\frac{25}{9}$

Option 4: $\frac{25}{18}$

Question : If $\tan\theta=1$, then the value of $\frac{8\sin\theta\:+\:5\cos\theta}{\sin^{3}\theta\:–\:2\cos^{3}\theta\:+\:7\cos\theta}$ is:

Option 1: $2$

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

Option 3: $3$

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

Question : Find the value of: $\sqrt{\frac{1 - \sin 3 \theta}{1 + \sin 3 \theta}}$

Option 1: $\sec 3 \theta - \tan 3 \theta$

Option 2: $(\sec 3 \theta - \tan 3 \theta)^3$

Option 3: $(\sec 3 \theta - \tan 3 \theta)^2$

Option 4: $\sec 3 \theta + \tan 3 \theta$

Question : If $\sec\theta-\tan\theta=\frac{1}{\sqrt3}$, then the value of $\sec\theta.\tan\theta$ is:

Option 1: $\frac{2}{3}$

Option 2: $\frac{2}{\sqrt3}$

Option 3: $\frac{4}{\sqrt3}$

Option 4: $\frac{1}{\sqrt3}$

Question : If $\sec \theta+\tan \theta=3$, then the value of $\sec \theta$ is:

Option 1: $\frac{4}{3}$

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

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

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