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PART - 1 CH - 3 Trigonometric Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSPART - 1 CH - 3 Trigonometric Functions1 Mark
Question
Write the value of $\sin \frac{5 \pi}{12} \sin \frac{\pi}{12}$.
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Answer


$\begin{aligned} \sin \frac{5 \pi}{12} \sin \frac{\pi}{12}= & \frac{1}{2}\left(2 \sin \frac{5 \pi}{12} \sin \frac{\pi}{12}\right) \\ & =\frac{1}{2}\left[\cos \left(\frac{5 \pi}{12}-\frac{\pi}{12}\right)-\cos \left(\frac{5 \pi}{12}+\frac{\pi}{12}\right)\right] \\ & =\frac{1}{2}\left(\cos \frac{\pi}{3}-\cos \frac{\pi}{2}\right) \\ & =\frac{1}{2}\left[\frac{1}{2}-0\right]=\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}\end{aligned}$

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