Question : Select the INCORRECT formula from the following options.

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

Option 2: $\sin^2 \theta+\cos^2 \theta=1$

Option 3: $\operatorname{cosec}^2 \theta-\cot^2 \theta=1$

Option 4: $\sec^2 \theta+\cos^2 \theta=1$

Question : Select the INCORRECT formula from the following options.

Option 1: $\operatorname{cosec}^2 \theta-\cot ^2 \theta=1$

Option 2: $\sin ^2 \theta+\cos ^2 \theta=1$

Option 3: $\sec ^2 \theta+\cos ^2 \theta=1$

Option 4: $\sec ^2 \theta-\tan ^2 \theta=1$

Question : Which of the following is equal to $[\frac{\cos \theta}{\sin \theta}+\frac{\sin \theta}{\cos \theta}]$?

Option 1: $\operatorname{cosec} \theta \sec \theta$

Option 2: $\sec \theta\tan \theta$

Option 3: $\operatorname{cosec} \theta\tan \theta$

Option 4: $\cot \theta \sec \theta$

Question : $\left(\frac{\tan ^3 \theta}{\sec ^2 \theta}+\frac{\cot ^3 \theta}{\operatorname{cosec}^2 \theta}+2 \sin \theta \cos \theta\right) \div\left(1+\operatorname{cosec}^2 \theta+\tan ^2 \theta\right), 0^{\circ}<\theta<90^{\circ}$, is equal to:

Option 1: $\operatorname{cosec} \theta \sec \theta$

Option 2: $\operatorname{cosec} \theta$

Option 3: $\sin \theta \cos \theta$

Option 4: $\sec \theta$

Question : $\frac{(1+\tan \theta+\sec \theta)(1+\cot \theta-\operatorname{cosec} \theta)}{(\sec \theta+\tan \theta)(1-\sin \theta)}$ is equal to:

Option 1: $2 \sec \theta$

Option 2: $2 \operatorname{cosec} \theta$

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

Option 4: $\sec \theta$

Question : The value of $\sqrt{\frac{1+\cos \theta}{1-\cos \theta}}$ is:

Option 1: $\sec\theta+\tan \theta$

Option 2: $\operatorname{cosec} \theta-\cot \theta$

Option 3: $\operatorname{cosec} \theta+\cot \theta$

Option 4: $\sec\theta-\tan \theta$