Consider a ΔABC in which ∠ C = 90°, ∠A = 60° and ∠ B = 30°.
Side AB will be the hypotenuse.
cos 60° = AC / AB -------[ cos 60° = 1/2]
So, AB = 2 AC -------------------------------(1)
Apply Pythagorean Theorem to find BC
AB² = BC² + AC²
4 AC² = BC² + AC²
So, BC = √3 AC ------------------------(2)
Now, we shall find the value of cos 30°
cos 30° = CB / AB
or, = √3 AC / 2 AC -------using equations (1) and (2)
So, cos 30° = √3 / 2
Hence, the exact value of
Since ∠A = 2∠B. So, cos 30° will be √3 / 2