sin-pi-24-cos-pi-24-cos-pi-12-

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

s i n \frac{π}{24} \cdot c o s \frac{π}{24} \cdot c o s \frac{π}{12} = ?

Answered by waiphyoemaung last updated on 08/Jul/21

solution

\sin \frac{π}{24} . \cos \frac{π}{24} . \cos \frac{π}{12}

= \frac{1}{2} . (2 \sin \frac{π}{24} \cos \frac{π}{24}) \cos \frac{π}{12}

= \frac{1}{2} . \sin \frac{π}{12} . \cos \frac{π}{12} (∵ \sin 2 α = 2 \sin α \cos α)

= \frac{1}{4} . 2 \sin \frac{π}{12} . \cos \frac{π}{12}

= \frac{1}{4} . \sin \frac{π}{6}

= \frac{1}{4} \times \frac{1}{2} (∵ \sin \frac{π}{6} = \frac{1}{2})

= \frac{1}{8}

Commented by mathdanisur last updated on 08/Jul/21

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