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Prove That: 2 Cos 5 π 12 Cos π 12 = 1 2

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Question

Prove that:

\[2\cos\frac{5\pi}{12}\cos\frac{\pi}{12} = \frac{1}{2}\]

Sum

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Solution

\[LHS = 2\left( \cos \frac{5\pi}{12} \right) \left( \cos \frac{\pi}{12} \right)\]
\[ = \cos \left( \frac{5\pi}{12} + \frac{\pi}{12} \right) + \cos \left( \frac{5\pi}{12} - \frac{\pi}{12} \right) \left[ \because 2 \cos A \cos B = \cos (A + B) + \cos (A - B) \right]\]
\[ = \cos \frac{\pi}{2} + \cos \frac{\pi}{3}\]
\[ = 0 + \frac{1}{2}\]
\[ = \frac{1}{2}\]
\[RHS = \frac{1}{2}\]
Hence, LHS = RHS

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Transformation Formulae

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Q 2.2 Q 2.1 Q 2.3

Chapter 8: Transformation formulae - Exercise 8.1 [Page 6]

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R.D. Sharma Mathematics [English] Class 11

Chapter 8 Transformation formulae
Exercise 8.1 | Q 2.2 | Page 6

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