Question

If sinθ = √3 cos θ, 0° < θ < 90°, then θ is equal to ?

Answer 1

Given:

• sinθ = √3cosθ .
• θ is acute i.e. 0°< θ<90°.

To Find:

• The measure of angle θ.

Concept Used:

• We will make use of value of some special angles in trigonometry.

Answer:

We are here given that ,

$\sf{\implies sin\theta=\sqrt{3}cos\theta}$

$\sf{\implies\dfrac{\sin\theta}{cos\theta}=\sqrt{3}}$

$\sf{\implies\tan\theta=\sqrt{3}}$

$\sf{\implies tan\theta=tan60^{\circ}}$

Eliminating tan both sides.

${\underline{\boxed{\red{\sf{\leadsto \theta=60^{\circ}}}}}}$

Some more values ,

• $\sf{\tan0^{\circ}=0}$
• $\sf{\tan30^{\circ}=\dfrac{1}{\sqrt{3}}}$
• $\sf{\tan60^{\circ}=\sqrt{3}}$
• $\sf{\tan90^{\circ}=\infty(Not\: Defined)}$