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If 3x = cosecθ and \(\frac{3}{\text{x}}\) = cotθ, find the value of 3 \((x^2-\frac{1}{x^2}).\) |
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Answer» Given that 3x = cosecθ and \(\frac{3}{x}\) = cotθ Now, cosec2θ = (3x)2 = 9x2. And cot2θ = \((\frac{3}{x})^2=\frac{9}{x^2}.\) We know that cosec2θ - cot2θ = 1 ∴ 9x2 - \(\frac{9}{x^2}=1\) ⇒ 9 \((x^2-\frac{1}{x^2})=1\) ⇒ 3 \((x^2-\frac{1}{x^2})=\frac{1}{3}.\) Hence, the value of 3 \((x^2-\frac{1}{x^2})\) is \(\frac{1}{3}.\) |
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