Question

Find the Value of$\frac{\cos 30^\circ - \sin 30^\circ}{\sin 60^\circ + \cos 60^\circ}$

• A. $$2-\sqrt{3}$$
• B. $$2+\sqrt{3}$$
• C. $$1-\sqrt{3}$$
• D. $$1+\sqrt{3}$$

Answer 1

Answer:

$$2-\sqrt{3}$$

Solution:

Given :

(cos 30° - sin 30°)/(sin 60° + cos 60°) 

Formula used :

Cos 30° = sin 60° = √3/2

cos 60° = sin 30° = 1/2 

Calculations :

Putting all values in the equation 

[(√3/2) - (1/2)]/[(√3/2) + (1/2)] 

⇒ (√3 - 1)/(√3 + 1)

Now rationalising 

⇒ [(√3 - 1)/(√3 + 1)] × [(√3 - 1)/(√3 - 1)]

⇒ (√3 - 1)²/2 

⇒ (3 + 1 - 2√3)/2 

⇒ (4 - 2√3)/2 

⇒ 2 - √3 

∴  Option A will be the correct answer.