Question

sin theta - cos theta/sin theta + cos theta = 1-root 3/1 + root3 find theta

Answer 1

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Answer 2

Answer:

The value of $\theta$ would be 30°

Step-by-step explanation:

Given expression,

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

By cross multiplication,

$(1+\sqrt{3})(\sin \theta - \cos\theta) = (1-\sqrt{3})(\sin \theta + \cos\theta)$

$\sin \theta+\sqrt{3}\sin \theta- \cos \theta -\sqrt{3}\cos\theta = \sin \theta -\sqrt{3}\sin \theta+\cos \theta - \sqrt{3}\cos \theta$

$\sqrt{3}\sin \theta- \cos \theta = -\sqrt{3}\sin \theta+\cos \theta$

$2\sqrt{3}\sin \theta = 2\cos \theta$

$\frac{\sin \theta}{\cos \theta}=\frac{1}{\sqrt{3}}$

$\tan \theta = \frac{1}{\sqrt{3}}$

$\implies \theta = 30^{\circ}$