Prove that $3 \sin \frac{\pi}{6} \sec \frac{\pi}{3} - 4 \sin \frac{5 \pi}{6} \cot \frac{\pi}{4} = 1$.

(N/A) We have the $L.H.S. = 3 \sin \frac{\pi}{6} \sec \frac{\pi}{3} - 4 \sin \frac{5 \pi}{6} \cot \frac{\pi}{4}$.
Using the values $\sin \frac{\pi}{6} = \frac{1}{2}$,$\sec \frac{\pi}{3} = 2$,$\sin \frac{5 \pi}{6} = \sin(\pi - \frac{\pi}{6}) = \sin \frac{\pi}{6} = \frac{1}{2}$,and $\cot \frac{\pi}{4} = 1$:
$L.H.S. = 3 \times \frac{1}{2} \times 2 - 4 \times \frac{1}{2} \times 1$
$L.H.S. = 3 - 2 = 1$
Since $L.H.S. = R.H.S. = 1$,the identity is proved.