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Trigonometric Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Functions3 Marks
Question
Prove that:
$\sin\frac{8\pi}{3}\cos\frac{23\pi}{6}+\cos\frac{13\pi}{3}\sin\frac{35\pi}{6}=\frac{1}{2}$
✓

Answer

$\text{L.H.S}=\sin\frac{8\pi}{3}\cos\frac{23\pi}{6}+\cos\frac{13\pi}{3}\sin\frac{35\pi}{6}$
$=\sin\Big(3\pi-\frac{\pi}{3}\Big)\cos\Big(4\pi-\frac{\pi}{6}\Big)+\cos\Big(4\pi+\frac{\pi}{3}\Big)\sin\Big(6\pi-\frac{\pi}{6}\Big)$
$=\sin\frac{\pi}{3}\cos\frac{\pi}{6}+\cos\frac{\pi}{3}\Big(-\sin\frac{\pi}{6}\Big)$ $(\because\sin(6\pi-\theta)=-\sin\theta)$
$=\frac{\sqrt{3}}{2}\times\frac{\sqrt{3}}{22}+\frac{1}{2}\times\Big(\frac{-1}{2}\Big)$
$=\frac{3}{2}-\frac{1}{4}$
$=\frac{2}{4}$
$=\frac{1}{2}$
$\text{= R.H.S}$
$\text{Proved}$

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