Find an acute angle θ when (cosθ − sin θ)/(cosθ+sin θ) = (1−√3)/(1+√3)

 Find an acute angle θ when (cosθ − sin θ)/(cosθ+sin θ) = (1−√3)/(1+√3)

 

given  (cosθ − sin θ)/(cosθ+sin θ) = (1−√3)/(1+√3)

 divide each term with cosθ on the LHS and use sinθ/cosθ =tanθ

we get

(1-tan θ)/(1+tanθ) = (1−√3)/(1+√3)

 rearrange and simplify

we get tan θ = √3

 θ =60 degrees

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