Question

If root 3 sin theta = cos theta, find value of theta

Answer 1

√3 sinθ = cosθ

sinθ = cosθ / √3

sinθ / cosθ = 1 / √3

Tanθ = 1 / √3

Tanθ = Tan30

θ = 30°

Answer 2

The value of θ is 30°.

Given,

The equation: $\sqrt{3} sin\theta=cos\theta$.

To Find,

The value of θ.

Solution,

The method of finding the value of θ in the equation is as follows -

We need to simplify the equation.

$\sqrt{3} sin\theta=cos\theta$ ⇒ $\frac{ sin\theta}{cos\theta}= \frac{1}{ \sqrt{3}}$ [Using cross multiple methods]

⇒ $tan\theta= \frac{1}{\sqrt{3} }$   [We know that  $\frac{sin\theta}{cos\theta} =tan\theta$ ]

⇒ $\theta = tan^{-1}(\frac{1}{\sqrt{3} } )$

$\theta=30$°. [Since, $\frac{1}{\sqrt{3} } =tan30$°]

Hence, the value of θ is 30°.

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