Question

If root 3 tan theta = 3 sin theta, find the value of sin theta

Answer 1

Answer:

Concept:

$Concept:sin^2\theta+cos^2\theta=1\\\\\sqrt{3}tan\theta=3sin\theta\\\\\sqrt{3}\frac{sin\theta}{cos\theta}=3sin\theta\\\\\frac{1}{cos\theta}=\frac{3}{\sqrt{3}}\\\\\frac{1}{cos\theta}=\sqrt{3}\\\\cos\theta=\frac{1}{\sqrt{3}}\\\\sin^2\theta=1-cos^2\theta\\\\sin^2\theta=1-\frac{1}{3}=\frac{2}{3}\\\\sin\theta=\sqrt{\frac{2}{3}}$

Answer 2

Answer:$sin \: \theta = \frac{ \sqrt{2} }{ \sqrt{3} }$

Solution:

$\sqrt{3} \: tan \: \theta = 3 \: sin \: \theta \\ \\ \frac{ \sqrt{3} }{3} \frac{sin \: \theta}{cos \: \theta} = sin \: \theta \\ \\ \frac{sin \: \theta}{ \sqrt{3}cos \: \theta } = sin \: \theta \\ \\ 1 = \sqrt{3} cos \: \theta \\ \\ \frac{1}{ \sqrt{3} } = \sqrt{1 - {sin}^{2}\theta } \\ \\ \frac{1}{3} = 1 - {sin}^{2} \theta \\ \\ {sin}^{2} \theta = \frac{2}{3} \\ \\ sin \: \theta = \frac{ \sqrt{2} }{ \sqrt{3} }$

Hope it helps you