Question : If $\tan \theta+\cot \theta=12$, then $\tan ^2 \theta+\cot ^2 \theta$ is:

Option 1: 66

Option 2: 128

Option 3: 142

Option 4: 132

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 : $(\sin \theta+\operatorname{cosec} \theta)^2+(\cos \theta+\sec \theta)^2=$?

Option 1: $5+\tan ^2 \theta+\cot ^2 \theta$

Option 2: $7+\tan ^2 \theta-\cot ^2 \theta$

Option 3: $7+\tan ^2 \theta+\cot ^2 \theta$

Option 4: $5+\tan ^2 \theta-\cot ^2 \theta$

Question : If $\theta$ is an acute angle and $\tan \theta+\cot \theta=2$, then the value of $\tan ^{200} \theta+\cot ^{200} \theta$ is:

Option 1: 1

Option 2: 2

Option 3: –1

Option 4: 0

Question : $\tan(θ -14\pi)$ is equal to:

Option 1: $\tan \theta$

Option 2: $-\cot \theta$

Option 3: $\cot \theta$

Option 4: $-\tan \theta$

Question : If $\tan\theta +\cot\theta =2$, then the value of $\left (\tan^{n}\theta+\cot^{n}\theta \right)$ is:

Option 1: $2^{n}$

Option 2: $2^{\frac{n}{2}}$

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

Option 4: $2$