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Given that cos θ = √3/2, then the value of \(\frac{cosec^2\,\theta - sec^2\,\theta}{cosec^2\,\theta + sec^2\,\theta}\) is :(cosec2θ - sec2θ)/(cosec2θ + sec2θ)(a) -1(b) 1(c) 1/2(d) - 1/2 |
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Answer» Correct answer is (c) 1/2 cos θ = √3/2 cos θ = cos 30° θ = 30° Now, \(\frac{cosec^2\,\theta - sec^2\,\theta}{cosec^2\,\theta + sec^2\,\theta}\) \(=\frac{cosec^2\,30^\circ - sec^2\,\theta}{cosec^2\,30^\circ + sec^2\,\theta}\) \(=\frac{(2)^2 - \left(\frac{2}{\sqrt{3}}\right)^2}{(2)^2 + \left(\frac{2}{\sqrt{3}}\right)^2}\) \(=\frac{4 - \frac{4}{3}}{4 + \frac{4}{3}}\) \(=\cfrac{\frac{12 - 4}{3}}{\frac{12 + 4}{3}}\) \(=\frac{8}{16}\) \(\Rightarrow \frac{1}{2}\) |
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