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AP EAMCET · Maths · Trigonometric Ratios & Identities

\(\cos ^2 10^{\circ}+\cos ^2 50^{\circ}-\sin 40^{\circ} \sin 80^{\circ}\) is equal to

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

Answer & Solution

Correct Answer

(D) \(\frac{3}{4}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { } \cos ^2 10^{\circ}+\cos ^2 50^{\circ}-\sin 40^{\circ} \sin 80^{\circ} \\ & =\frac{1}{2}\left[2 \cos ^2 10^{\circ}+2 \cos ^2 50^{\circ}-2 \sin 40^{\circ} \sin 80^{\circ}\right] \\ & =\frac{1}{2}\left[1+\cos 20^{\circ}+1+\cos 100^{\circ}\right. \\ &…