A)
B) 0
C)
D)
Correct Answer: A
Solution :
\[{{\cos }^{2}}\left( \frac{\pi }{6}+\theta \right)-\,\,si{{n}^{2}}\left( \frac{\pi }{6}-\theta \right)\] \[=\cos \left( \frac{\pi }{6}+\theta +\frac{\pi }{6}-\theta \right)\,\cos \,\left( \frac{\pi }{6}+\theta -\frac{\pi }{6}+\theta \right)\] \[\left[ \because \,co{{s}^{2}}A - si{{n}^{2}}\,B = cos\left( A + B \right) cos\left( A - B \right) \right]\] \[= cos \frac{2\pi }{6} cos 2\theta = \frac{1}{2} cos 2\theta \]
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