Q.Find the value of $\tan 75^\circ$.

The compound-angle formulae expand $\sin(A\pm B)$, $\cos(A\pm B)$ and $\tan(A\pm B)$ in terms of the individual ratios of $A$ and $B$: $\sin(A\pm B)=\sin A\cos B\pm\cos A\sin B$, $\cos(A\pm B)=\cos A\cos B\mp\sin A\sin B$, $\tan(A\pm B)=\dfrac{\tan A\pm\tan B}{1\mp\tan A\tan B}$. Their main practical use is finding the exact ratios of angles that are not in the standard table by writing them …