Prove that: 3 6 3 -4 5 6 4 =1 - Vidyadip

Question

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

✓

Answer

$\text{L.H.S}=3\sin\frac{\pi}{6}\sec\frac{\pi}{3}-4\sin\frac{5\pi}{6}\cot\frac{\pi}{4}$
$=3\times\frac{1}{2}\times2-4\sin\Big(\pi-\frac{\pi}{6}\Big)\times1$
$=3-4\sin\frac{\pi}{6}$
$=3-4\times\frac{1}{2}$
$= 3 - 2$
$= 1$
$\text{= R.H.S}$
$\text{Proved}$

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