cos theeta-sin theeta /cos theeta+sin theeta=1-√3/1+√3a.
Answers
Answer:
The value of \thetaθ would be 30°
Step-by-step explanation:
Given expression,
\frac{\sin \theta - \cos\theta}{\sin \theta + \cos \theta}=\frac{1-\sqrt{3}}{1+\sqrt{3}}
sinθ+cosθ
sinθ−cosθ
=
1+
3
1−
3
By cross multiplication,
(1+\sqrt{3})(\sin \theta - \cos\theta) = (1-\sqrt{3})(\sin \theta + \cos\theta)(1+
3
)(sinθ−cosθ)=(1−
3
)(sinθ+cosθ)
\sin \theta+\sqrt{3}\sin \theta- \cos \theta -\sqrt{3}\cos\theta = \sin \theta -\sqrt{3}\sin \theta+\cos \theta - \sqrt{3}\cos \theta sinθ+
3
sinθ−cosθ−
3
cosθ=sinθ−
3
sinθ+cosθ−
3
cosθ
\sqrt{3}\sin \theta- \cos \theta = -\sqrt{3}\sin \theta+\cos \theta
3
sinθ−cosθ=−
3
sinθ+cosθ
2\sqrt{3}\sin \theta = 2\cos \theta2
3
sinθ=2cosθ
\frac{\sin \theta}{\cos \theta}=\frac{1}{\sqrt{3}}
cosθ
sinθ
=
3
1
\tan \theta = \frac{1}{\sqrt{3}}tanθ=
3
1
\implies \theta = 30^{\circ}⟹θ=30
∘