मराठी

Write the Value of Cos π 7 Cos 2 π 7 Cos 4 π 7 .

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प्रश्न

Write the value of \[\cos\frac{\pi}{7} \cos\frac{2\pi}{7} \cos\frac{4\pi}{7} .\]

  
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उत्तर

\[\text{ We have } , \]
\[ \cos\frac{\pi}{7} \cos\frac{2\pi}{7} \cos\frac{4\pi}{7} = \frac{2\sin\frac{\pi}{7} \cos\frac{\pi}{7} \cos\frac{2\pi}{7} \cos\frac{4\pi}{7}}{2\sin\frac{\pi}{7}} \]
\[ \left[ \text{ On dividing and multiplying by  } 2\sin\frac{\pi}{7} \right]\]
\[ = \frac{2 \times \sin\frac{2\pi}{7} \cos\frac{2\pi}{7} \cos\frac{4\pi}{7}}{2 \times 2\sin\frac{\pi}{7}}\]

Proceeding in the same way, we get

\[\cos\frac{\pi}{7} \cos\frac{2\pi}{7} \cos\frac{4\pi}{7} = \frac{\sin\frac{8\pi}{7}}{8\sin\frac{\pi}{7}}\]
\[ = \frac{\sin\left( \pi + \frac{\pi}{7} \right)}{8\sin\frac{\pi}{7}}\]
\[ = \frac{- \sin\frac{\pi}{7}}{8\sin\frac{\pi}{7}}\]
\[ \therefore \cos\frac{\pi}{7} \cos\frac{2\pi}{7} \cos\frac{4\pi}{7} = \frac{- 1}{8}\]

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Values of Trigonometric Functions at Multiples and Submultiples of an Angle
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पाठ 9: Values of Trigonometric function at multiples and submultiples of an angle - Exercise 9.4 [पृष्ठ ४२]

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आर.डी. शर्मा Mathematics [English] Class 11
पाठ 9 Values of Trigonometric function at multiples and submultiples of an angle
Exercise 9.4 | Q 10 | पृष्ठ ४२

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