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If 3x = cosec θ and \(\frac{3}{x}=\cot \theta\), find the value of \(3\left(x^2-\frac{1}{x^2}\right)\)1. \(\frac{1}{2}\)2. \(\frac{1}{3}\)3. 24. 3 |
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Answer» Correct Answer - Option 2 : \(\frac{1}{3}\) Given: 3x = cosecθ and 3/x = cotθ Formula used: cosec2θ – cot2θ = 1 Calculation: ⇒ (3x)2 – (3/x)2 = 1 ⇒ 9(x2 – 1/x2) = 1 ⇒ (x2 – 1/x2) = 9 ⇒ 3(x2 – 1/x2) = 1/3 ∴ Required value is \(\frac{1}{3}\) |
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