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COMEDK · Maths · 8. Trigonometric Ratios & Identities

The value of \(\dfrac{\sin ^2 20^{\circ}+\cos ^4 20^{\circ}}{\sin ^4 20^{\circ}+\cos ^2 20^{\circ}}\) is

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

Answer & Solution

Correct Answer

(D) \(1\)

Step-by-step Solution

Detailed explanation

Let \(\theta = 20^{\circ}\). The expression is \(E = \dfrac{\sin^{2}\theta + \cos^{4}\theta}{\sin^{4}\theta + \cos^{2}\theta}\). Using the identity \(\sin^{2}\theta = 1 - \cos^{2}\theta\), we substitute into the numerator: Numerator…