The value of cos^2(π/6 + x) - sin^2(π/6 - x)

Question

The value of cos²\(\left(\frac{\pi}{6}+x \right)\) - sin²\(\left(\frac{\pi}{6}-x \right)\) is

A. \(\frac{1}{2}\) cos 2x

B. 0

C. \(-\frac{1}{2}\) cos 2x

D. \(\frac{1}{2}\)

Answer 1

Correct answer is A.

Given expression is  cos²\(\left(\frac{\pi}{6}+x \right)\) - sin²\(\left(\frac{\pi}{6}-x \right)\)

[using the identity sin² x + cos² x = 1]

[using the formula a² + b² = (a + b)² – 2ab]

[Using the identity cos (A + B) – cos (A - B) = -2sinA sinB ]

[multiplying and dividing the term cos² x with 2]