Trigonometry

Find the value of $\dfrac{2\tan30^\circ}{1-\tan^230^\circ}$.

If $\cos\theta=\dfrac{7}{25}$, then the value of $\tan\theta$ is:

The value of $\tan1^\circ\tan2^\circ\tan3^\circ\cdots\tan89^\circ$ is:

The value of $(\text{cosec}\theta-\sin\theta)(\sec\theta-\cos\theta)(\tan\theta+\cot\theta)$ is:

The greatest value of $3\sin\theta+4\cos\theta+5$ (for $0^\circ\le\theta\le90^\circ$) is: