Question

If root 3 tanθ = 3sinθ, find the value of sinθ

Answer 1

Step-by-step explanation:

Given  

If root 3 tanθ = 3 sinθ, find the value of sinθ

• Given √3 tan θ = 3 sin θ
•   Now √3 sin θ  / cos θ  = 3 sin θ  
•    So cos θ  = 1/ √3
• Squaring both sides we get  
•  Cos^2 θ = 1/3
• So 1 – sin ^2 θ  = 1/3
• Or sin^2 θ  = 1 – 1/3
• So sin^2 θ  = 2/3
• So sin θ  = ±√ 2/3

Answer 2

Answer:

The required value is $sin\theta=\pm\sqrt{\frac{2}{3}}$

Step-by-step explanation:

Consider the provided trigonometry functions

$\sqrt{3} tan\theta = 3 sin\theta$

$\sqrt{3}( \frac{sin\theta}{cos\theta}) = 3 sin\theta$

Divide both sides by ✓3 sinθ

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

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

Squaring on both sides:

$cos^2\theta=(\frac{1}{\sqrt{3}})^2$

$cos^2\theta=\frac{1}{3}$

Substitute Cos²θ = 1-sin²θ

$1-sin^2\theta=\frac{1}{3}$

$sin^2\theta=1-\frac{1}{3}$

$sin^2\theta=\frac{2}{3}$

$sin\theta=\pm\sqrt{\frac{2}{3}}$

Hence, the required value is $sin\theta=\pm\sqrt{\frac{2}{3}}$