Question

Find the value
of trigonometric ratio
COS22 1/2°​

Answer 1

22½° lies in the first quadrant.

Therefore, sin 22½° is positive.

For all values of the angle A we know that, cos A = 2 cos2 A2 - 1

⇒ 1 + cos A = 2 cos2 A2

⇒ 2 cos2 A2 = 1 + cos A

⇒ 2 cos2 22½˚ = 1 + cos 45°

⇒ cos2 22½˚ = 1+cos45°2

⇒ sin2 22½˚ = 1+12√2, [Since we know cos 45° = 1√2]

⇒ cos 22½˚ = 12(1+12√)−−−−−−−−√, [Since, cos 22½˚ > 0]

⇒ cos 22½˚ = 2√+122√−−−−√

⇒ cos 22½˚ = 122+2–√−−−−−−√

Therefore, cos 22½˚ = 122+2–√−−−−−−√