मराठी

The Value of Cos 2 ( π 6 + X ) − Sin 2 ( π 6 − X ) is

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प्रश्न

The value of \[\cos^2 \left( \frac{\pi}{6} + x \right) - \sin^2 \left( \frac{\pi}{6} - x \right)\] is

 

पर्याय

  • \[\frac{1}{2} \cos 2 x\]

     

  • 0

  • \[- \frac{1}{2} \cos 2 x\]

     

  • \[\frac{1}{2}\]

     

MCQ
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उत्तर

\[\frac{1}{2}\cos 2x\]

\[\cos^2 \left( \frac{\pi}{6} + x \right) - \sin^2 \left( \frac{\pi}{6} - x \right)\]
\[ = \cos\left( \frac{\pi}{6} + x + \frac{\pi}{6} - x \right)\cos\left( \frac{\pi}{6} + x - \frac{\pi}{6} + x \right) \left[\text{ Using }\cos(A + B) \cos(A - B) = \cos^2 A - \sin^2 B \right]\]
\[ = \cos\frac{2\pi}{6}\cos2x\]
\[ = \frac{1}{2}\cos2x \left[ \text{ As }\cos\frac{\pi}{3} = \frac{1}{2} \right]\]

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पाठ 7: Values of Trigonometric function at sum or difference of angles - Exercise 7.4 [पृष्ठ २८]

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आर.डी. शर्मा Mathematics [English] Class 11
पाठ 7 Values of Trigonometric function at sum or difference of angles
Exercise 7.4 | Q 12 | पृष्ठ २८

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