If 3 sin θ-cos θ=0 where 0<θ<90∘, then find the value of θ.

If $\sqrt{3} \sin θ - \cos θ = 0$ where $0 < θ < 90^{\circ}$ , then find the value of θ.

A
$45^{\circ}$
B
$40^{\circ}$
C
$30^{\circ}$
D
$35^{\circ}$

Solution:

Given,

\sqrt{3} \sin θ - \cos θ = 0

where

0 < θ < 90^{\circ}

.
Use the identity,

\tan θ = \frac{\sin θ}{\cos θ}

.
Evaluating the given expression.

\sqrt{3} \sin θ - \cos θ = 0

\Rightarrow \sqrt{3} \sin θ = \cos θ

\Rightarrow \frac{\sin θ}{\cos θ} = \frac{1}{\sqrt{3}}

\Rightarrow \tan θ = \frac{1}{\sqrt{3}}

\Rightarrow θ = 30^{\circ}

Therefore, the value of

θ

is

30^{\circ}

.
Hence, option 3 is correct.

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