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TS EAMCET · Maths · Trigonometric Ratios & Identities

If \(2 \tan ^2 \theta-4 \sec \theta+3=0\), then \(2 \sec \theta=\)

  1. A \(3\)
  2. B \(2+\sqrt{2}\) and \(2-\sqrt{2}\)
  3. C \(2-\sqrt{2}\)
  4. D \(2+\sqrt{2}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(2+\sqrt{2}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & 2 \tan ^2 \theta-4 \sec \theta+3=0 \\ & \Rightarrow 2 \sec ^2 \theta-4 \sec \theta+1=0 \\ & \Rightarrow \sec \theta=\frac{4 \pm \sqrt{16-8}}{4} \Rightarrow \sec \theta=\frac{2 \pm \sqrt{2}}{2} \\ &|\sec \theta|\gt1 \Rightarrow \sec \theta \neq…