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  4. cos2 ((π/6) + θ) - sin2 ((π/6) - θ) =

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Q. $\cos^{2} \left(\frac{\pi}{6} + \theta\right) - \sin^{2} \left(\frac{\pi}{6} - \theta\right) = $

BITSATBITSAT 2014

Solution:

$\cos^{2} \left(\frac{\pi}{6} + \theta\right) - \sin^{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) $
$= \cos \frac{2\pi}{6} \cos2 \theta = \frac{1}{2} \cos2\theta$