Question

Prove that :

\[ \tan4\pi-\cos\frac{3\pi}{2}-\sin\frac{5\pi}{6}\cos\frac{2\pi}{3} = \frac14 \]

Solution

\[ \begin{aligned} &\tan4\pi-\cos\frac{3\pi}{2}-\sin\frac{5\pi}{6}\cos\frac{2\pi}{3} \\[8pt] =& 0-0-\left(\frac12\right)\left(-\frac12\right) \\[8pt] =& \frac14 \end{aligned} \]

Hence Proved.