Question

find an acute angle theta if cosec theta + sec theta / cosec theta - sec theta= root 3 + 1 / root 3 - 1​

Answer 1

Answer:

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Step-by-step explanation:

$to \: find : \\ acute \: angle \: \\ \\ so \: here \\ \\ \frac{cosec \: θ + sec \: θ}{cosec \: θ - sec \: θ} = \frac{ \sqrt{3} + 1}{ \sqrt{3} - 1 } \\ \\ applying \: now \: \\ componendo \: dividendo \\ we \: get \\ \\ \frac{cosec \: θ + sec \:θ + cosec \: θ - sec \:θ }{cosec \: θ + sec \: θ - (cosec \: θ - sec \:θ) } = \frac{ \sqrt{3} + 1 + \sqrt{3} - 1 }{ \sqrt{3} + 1 - ( \sqrt{3} - 1) } \\ \\ = \frac{cosec \:θ + cosec \: θ}{cosec \: θ + sec \: θ - cosec \:θ + sec \: θ} = \frac{ \sqrt{3} + \sqrt{3} }{ \sqrt{ 3 } + 1 - \sqrt{ 3 } + 1} \\ \\ = \frac{2.cosec \:θ }{2.sec \: θ} = \frac{2. \sqrt{3} }{2} \\ \\ = \frac{cosec \: θ}{sec \: θ} = \sqrt{3} \\ \\ we \: know \: that \\ \\ cot \: θ = \frac{cosec \:θ }{sec \:θ } \\ \\ thus \: then \\ \\ cot \: θ = \sqrt{3} \\ \\ we \: have \\ \\ cot \: 30 = \sqrt{3} \\ \\ henceforth \\ \\ θ = 30$