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प्रश्न
If `cot theta = 3/4`, prove that `sqrt((sec theta - cosec theta)/(sec theta + cosec theta)) = 1/sqrt7`
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उत्तर
`cot theta = "𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒"/"𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒"`
Let x be the hypotenuse by applying Pythagoras theorem.
𝐴𝐶2 = 𝐴𝐵2 + 𝐵𝐶2
𝑥2 = 16 + 9
`x^2 = 25 => x = 5`
`sec theta = (AC)/(BC) = 5/3`
`cosec theta = (AC)/(AB) = 5/4`
On substituting in equation we get
`sqrt((sec theta - cosec theta)/(sec theta + cosec theta)) = sqrt((5/3 - 5/4)/(5/3 + 5/4))`
`= sqrt(((20 - 15)/12)/((20 + 15)/12)) = sqrt(5/35) = 1/sqrt7`
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