Question : Simplify $\frac{\cos ^4 \theta-\sin ^4 \theta}{\sin ^2 \theta}$.

Option 1: $1-\tan ^2 \theta$

Option 2: $\tan ^2 \theta-1$

Option 3: $\cot ^2 \theta-1$

Option 4: $1-\cot ^2 \theta$

Question : $\sqrt{\frac{1+\sin\theta}{1-\sin\theta}}+\sqrt{\frac{1-\sin\theta}{1+\sin\theta}}$ is equal to:

Option 1: $2\cos\theta$

Option 2: $2\sin\theta$

Option 3: $2\cot\theta$

Option 4: $2\sec\theta$

Question : Find the value of $\left(\tan ^2 \theta+\tan ^4 \theta\right)$.

Option 1: $\cot ^2 \theta-\tan ^2 \theta$

Option 2: $\ {\sec}^4 \theta-\ {\sec}^2 \theta$

Option 3: $\ {\sec}^4 \theta-\ {\sec}^4 \theta$

Option 4: $ \ {\sec}^4 \theta+\ {\sec}^2 \theta$

Question : If $\frac{\cos \theta}{1-\sin \theta}+\frac{\cos \theta}{1+\sin \theta}=4,0^{\circ}<\theta<90^{\circ}$, then what is the value of $(\sec \theta+\operatorname{cosec} \theta+\cot \theta) ?$

Option 1: $1+2 \sqrt{3}$

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

Option 3: $\frac{2+\sqrt{3}}{3}$

Option 4: $2+\sqrt{3}$

Question : If $\cos ^2 \theta-\sin ^2 \theta=\tan ^2 \phi$, then which of the following is true?

Option 1: $\cos \theta \cos \phi=1$

Option 2: $\cos ^2 \phi-\sin ^2 \phi=\tan ^2 \theta$

Option 3: $\cos ^2 \phi-\sin ^2 \phi=\cot ^2 \theta$

Option 4: $\cos \theta \cos \phi=\sqrt{2}$