Question : What will be the value of $\cos x \operatorname{cosec} x - \sin x \sec x$?

Option 1: $\cot \frac{2x}{2}$

Option 2: $\tan 2 x $

Option 3: $\cot 2 x $

Option 4: $ 2 \cot 2x$

Question : If $\cos^2x+\cos^4x=1$, then $\tan^2x+\tan^4x$?

Option 1: $0$

Option 2: $1$

Option 3: $2 \tan^2x$

Option 4: $2\tan^4x$

Question : The value of tan 25° tan 35° tan 45° tan 55° tan 65° is:

Option 1: $2$

Option 2: $1$

Option 3: $\sqrt{3}$

Option 4: $0$

Question : If $\tan\theta-\cot\theta=0$ and $\theta$ is positive acute angle, then the value of $\frac{\tan(\theta+15)}{\tan(\theta-15)}$ is:

Option 1: $3$

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

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

Option 4: $\sqrt{3}$

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