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Prove That: Sin ( 4 π 9 + 7 ) Cos ( π 9 + 7 ) − Cos ( 4 π 9 + 7 ) Sin ( π 9 + 7 ) = √ 3 2

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प्रश्न

Prove that:

\[\sin\left( \frac{4\pi}{9} + 7 \right)\cos\left( \frac{\pi}{9} + 7 \right) - \cos\left( \frac{4\pi}{9} + 7 \right)\sin\left( \frac{\pi}{9} + 7 \right) = \frac{\sqrt{3}}{2}\]

 

संक्षेप में उत्तर
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उत्तर

LHS = \[\sin\left( \frac{4\pi}{9} + 7 \right)\cos\left( \frac{\pi}{9} + 7 \right) - \cos\left( \frac{4\pi}{9} + 7 \right)\sin\left( \frac{\pi}{9} + 7 \right)\]
\[ = \sin\left[ \left( \frac{4\pi}{9} + 7 \right) - \left( \frac{\pi}{9} + 7 \right) \right] \left[ \sin A\cos B - \cos A\sin B = \sin\left( A - B \right) \right]\]
\[ = \sin\frac{3\pi}{9}\]
\[ = \sin\frac{\pi}{3}\]
\[ = \frac{\sqrt{3}}{2}\]
= RHS

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अध्याय 7: Values of Trigonometric function at sum or difference of angles - Exercise 7.1 [पृष्ठ १९]

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आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 7 Values of Trigonometric function at sum or difference of angles
Exercise 7.1 | Q 12.2 | पृष्ठ १९

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