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:

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 $\cos^2 \theta=\frac{3}{4}$, where $\theta$ is an acute angle, then the value of $\sin \left(\theta+30^{\circ}\right)$ is:

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