cos^2 ((π)/6+θ )-sin^2 ((π)/6-θ )=

Correct answer: (A) 1/2 cos 2 θ. cos^2 ((π)/6+θ )-sin^2 ((π)/6-θ ) =cos ((π)/6+θ+(π)/6-θ ) cos ((π)/6+θ-(π)/6+θ ) =cos (2 π)/6 cos 2 θ=1/2 cos 2 θ

Q43 / 125 · BITSAT 2014 · Mathematics

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

Correct answer
A
$\frac{1}{2} \cos 2 \theta$
B
0
C
$-\frac{1}{2} \cos 2 \theta$
D
$\frac{1}{2}$

Solution

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

Hence, the correct answer is option: 'A'.

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