If $\theta$ does not lie in the second quadrant and $\tan \theta = \frac{-3}{4}$,then $\tan \frac{\theta}{2} + \sin 2 \theta =$

If $\sin(\frac{\pi}{18}) \sin(\frac{5\pi}{18}) \sin(\frac{7\pi}{18}) = K$,then the value of $\sin(\frac{10K\pi}{3})$ is :

If $L = \sin^{2}\left(\frac{\pi}{16}\right) - \sin^{2}\left(\frac{\pi}{8}\right)$ and $M = \cos^{2}\left(\frac{\pi}{16}\right) - \sin^{2}\left(\frac{\pi}{8}\right)$,then which of the following is correct?

If $\tan \theta = \frac{a}{b}$,then $b \cos 2 \theta + a \sin 2 \theta = $

Find the value of $\tan \frac{\pi}{8}$.

Let $f_n(x) = \tan \frac{x}{2}(1 + \sec x)(1 + \sec 2x) \dots (1 + \sec 2^n x)$,then