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The Value of Cos 2 ( π 6 + X ) − Sin 2 ( π 6 − X ) is - CBSE (Science) Class 11 - Mathematics

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Question

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

 
  • \[\frac{1}{2} \cos 2 x\]

     

  • 0

  • \[- \frac{1}{2} \cos 2 x\]

     

  • \[\frac{1}{2}\]

     

Solution

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

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

  Is there an error in this question or solution?

APPEARS IN

 RD Sharma Solution for Mathematics Class 11 (2019 to Current)
Chapter 7: Values of Trigonometric function at sum or difference of angles
Q: 12 | Page no. 28
Solution The Value of Cos 2 ( π 6 + X ) − Sin 2 ( π 6 − X ) is Concept: Trigonometric Functions of Sum and Difference of Two Angles.
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