Question : If $\sec \theta+\cos \theta=32$, then $\sec^2 \theta+\cos^2 \theta$ is:

Option 1: 1000

Option 2: 1022

Option 3: 1024

Option 4: 1020

Question : $\frac{\sin ^2 \theta}{\cos \theta(1+\cos \theta)}+\frac{1+\cos \theta}{\cos \theta}=$?

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

Option 2: $\sec\theta$

Option 3: $2\cos\theta$

Option 4: $2\sec\theta$

Question : If $\tan ^2 \theta+\tan ^4 \theta=1$, then:

Option 1: $\cot ^2 \theta+\cot ^4 \theta=1$

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

Option 3: $\sin ^2 \theta+\sin ^4 \theta=1$

Option 4: $\operatorname{cosec}^2 \theta+\sec ^4 \theta=1$

Question : $ \sqrt{\frac{1+\cos \theta}{1-\cos \theta}}+\sqrt{\frac{1-\cos \theta}{1+\cos \theta}}=$________.

Option 1: $2 \sin \theta$

Option 2: $2 \cos \theta$

Option 3: $ 2 \operatorname{cosec} \theta $

Option 4: $2 \sec \theta$

Question : If $x+\frac{1}{x}=2 \cos \theta$, then $x^3+\frac{1}{x^3}=?$

Option 1: $2 \cos 2θ$

Option 2: $\cos 3θ$

Option 3: $2 \cos 3θ$

Option 4: $\cos 2θ$

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

Option 1: $1-\cos \theta$

Option 2: $1-\sin \theta$

Option 3: $\cos \theta$

Option 4: $\sin \theta$