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Question
if `cot theta = 3/4` prove that `sqrt((sec theta - cosec theta)/(sec theta +cosec theta)) = 1/sqrt7`
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Solution
`cot theta = "๐๐๐๐๐๐๐๐ก ๐ ๐๐๐"/"๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐"`
Let x be the hypotenuse by applying Pythagoras theorem.
๐ด๐ถ2 = ๐ด๐ต2 + ๐ต๐ถ2
๐ฅ2 = 16 + 9
`x^2 = 25 => x = 5`
`sec theta = (AC)/(AB) = 5/4`
`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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