Question : Which of the following is a FALSE statement?

Option 1: $\tan ^2 \mathrm{~A}=1-\sec ^2 \mathrm{~A}$

Option 2: $\sin \mathrm{A}=\tan \mathrm{A} \times \cos \mathrm{A}$

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

Option 4: $\cos A \times \sec A=1$

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

Option 1: $\sec A – \tan A$

Option 2: $\operatorname{cosec} A + \cot A$

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

Option 4: $\operatorname{cosec} A – \cot A$

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

Option 1: $ \sin \theta+\cos \theta$

Option 2: $\sin \theta \cos \theta$

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

Option 4: $\sec \theta+\operatorname{cosec} \theta$

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: $\sec\theta-\tan \theta$

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: $\sec \theta$