Question : If $\sin(3\alpha -\beta )=1$ and $\cos(2\alpha+\beta)=\frac{1}{2}$, then the value of $\tan \alpha$ is:

Question : If $\alpha$ and $\beta$ are positive acute angles, $\sin (4\alpha -\beta )=1$ and $\cos (2\alpha +\beta)=\frac{1}{2}$, then the value of $\sin (\alpha +2\beta)$ is:

Question : If $\cos^{2}\alpha-\sin^{2}\alpha=\tan^{2}\beta$, then the value of $\cos^{2}\beta-\sin^{2}\beta$ is:

Question : If $\sin \alpha=\frac12$ and $\sin \beta=\frac12$, then what is the value of $\cos (\alpha+\beta)$? $(0°<\alpha, \beta<90° )$

Question : If $\cos 5 \alpha=\sin \alpha$ and $5 \alpha<90^{\circ}$, then the value of $\tan 2 \alpha$ is: