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TS EAMCET · Maths · Trigonometric Ratios & Identities

\(\cos ^2 76^{\circ}+\cos ^2 16^{\circ}-\cos 76^{\circ} \cos 16^{\circ}\) is equal to

  1. A \(0\)
  2. B \(\frac{1}{2}\)
  3. C \(-\frac{1}{4}\)
  4. D \(\frac{3}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{3}{2}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \cos ^2 76^{\circ}+\cos ^2 16^{\circ}-\cos 76^{\circ} \cos 16^{\circ} \\ & =\cos ^2 76^{\circ}+1-\sin ^2 16^{\circ}-\frac{1}{2} \cdot 2 \cos 76^{\circ} \cos 16^{\circ} \\ & =1+\cos \left(76^{\circ}+16^{\circ}\right) \cos \left(76^{\circ}-16^{\circ}\right) \\ &…