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Question
Find an acute angle θ when `(cos θ - sin θ)/(cos θ + sin θ) = (1 - sqrt(3))/(1 + sqrt(3))`
Solution
Given, `(cos θ - sin θ)/(cos θ + sin θ) = (1 - sqrt(3))/(1 + sqrt(3))`
Cross multiplying
`(1 + sqrt(3)) (cos θ - sin θ) = (1 - sqrt(3)) (cos θ + sin θ)`
`1(cos θ - sin θ) + sqrt(3)(cos θ - sin θ) = 1(cosθ + sin θ) - sqrt(3) (cos θ + sin θ)`
`cos θ - sin θ + sqrt(3)cos θ - sqrt(3)sin θ = cos θ + sin θ - sqrt(3) cos θ - sqrt(3)sin θ - sin θ + sqrt(3)cos θ = sin θ - sqrt(3)cos θ`
`sqrt(3)cos θ + sqrt(3) cos θ` = sin θ + sin θ
`2sqrt(3)cos θ` = 2 sin θ
`sqrt(3)cos θ` = sin θ
`sqrt(3) = sinθ/cosθ`
tan θ = `sqrt(3)`
Since tan 60° = `sqrt(3)`
Therefore, θ = 60°
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= `1/square + square/square`
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