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Question Number 145852 by mathdanisur last updated on 08/Jul/21

$$sin\frac{\pi }{24}\cdot cos\frac{\pi }{24}\cdot cos\frac{\pi }{12}=?$$

Answered by waiphyoemaung last updated on 08/Jul/21

$$\mathrm{solution}$$$$\sin \frac{\pi }{24}.\cos \frac{\pi }{24}.\cos \frac{\pi }{12}$$$$=\frac{1}{2}.\left(2\sin \frac{\pi }{24}\cos \frac{\pi }{24}\right)\cos \frac{\pi }{12}$$$$=\frac{1}{2}.\sin \frac{\pi }{12}.\cos \frac{\pi }{12}(\because \sin 2\alpha =2\sin \alpha \cos \alpha )$$$$=\frac{1}{4}.2\sin \frac{\pi }{12}.\cos \frac{\pi }{12}$$$$=\frac{1}{4}.\sin \frac{\pi }{6}$$$$=\frac{1}{4}\times \frac{1}{2}(\because \sin \frac{\pi }{6}=\frac{1}{2})$$$$=\frac{1}{8}$$

Commented by mathdanisur last updated on 08/Jul/21

$$ThanksSercool$$

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