COMEDK · Maths · 8. Trigonometric Ratios & Identities
Simplified expression of \(\cos ^2\left(\dfrac{\pi}{6}+\theta\right)-\sin ^2\left(\dfrac{\pi}{6}-\theta\right)\) is
- A \(-\dfrac{\sqrt{3}}{2} \cos 2 \theta\)
- B \(\dfrac{1}{2} \cos 2 \theta\)
- C \(\dfrac{\sqrt{3}}{2} \cos 2 \theta\)
- D \(\dfrac{1}{2} \sin 2 \theta\)
Answer & Solution
Correct Answer
(B) \(\dfrac{1}{2} \cos 2 \theta\)
Step-by-step Solution
Detailed explanation
The given expression is \(\cos^{2}\left(\dfrac{\pi}{6} + \theta\right) - \sin^{2}\left(\dfrac{\pi}{6} - \theta\right)\). Using the trigonometric identity \(\cos^{2} A - \sin^{2} B = \cos(A + B) \cos(A - B)\), we set \(A = \dfrac{\pi}{6} + \theta\) and…
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