1.

If \(2x = \sin \theta \) and \(\frac{2}{x} =\cos \theta \), then the value of \(4\left( {{x^2} + \frac{1}{{{x^2}}}} \right)\) is:1. 12. 03. 24. 4

Answer» Correct Answer - Option 1 : 1

Given:

2x = sinθ

2/x = cosθ

Formula used:

Sin2θ + Cos2θ = 1

Calculation:

2x = sinθ

⇒ 4x2 = sin2θ

2/x = cosθ

⇒ 4/x2 = cos2θ

Sin2θ + Cos2θ = 4x2 + 4/x2 

⇒ 1 = 4x2 + 4/x2 

⇒ 1 = 4(x2 + 1/x2)

∴ Required value is 1


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