Question : If $\theta$ is a positive acute angle and $4\sin^{2}\theta =3$, then the value of $\left (\tan\theta-\cot\frac{\theta}{2}\right)$ is:

Question : If $\theta$ is a positive acute angle and $3(\sec^{2}\theta+\tan^{2}\theta)=5$, then the value of $\cos2\theta$ is:

Question : If $2 \cot \theta = 3$, find the value of $\frac{\sqrt{13} \sin \theta – 3 \tan \theta}{3 \tan \theta + \sqrt{13} \cos \theta}$

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

Question : $\theta$ is a positive acute angle and $\sin\theta-\cos\theta=0$, then the value of $\sec\theta+\operatorname{cosec}\theta$ is: