Find an acute angle when Introduction to Trigonometry

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Solution

Q.
Find an acute angle $θ$ when $\frac{\cos θ - \sin θ}{\cos θ + \sin θ} = \frac{1 - \sqrt{3}}{1 + \sqrt{3}}$

Ans.
$(60 °)$

$\frac{\cos θ - \sin θ}{\cos θ + \sin θ} = \frac{1 - \sqrt{3}}{1 + \sqrt{3}}$

Dividing the numerator and denominator of LHS by $\cos θ,$ we get

$\frac{1 - \tan θ}{1 + \tan θ} = \frac{1 - \sqrt{3}}{1 + \sqrt{3}}$

Which on simplification (or comparison) gives

$\tan θ = \sqrt{3} \Rightarrow θ = 60 °$

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