Question

using half angle formula, find the
value of sin 22 and half degree​

Answer 1

Answer:

Solution:

22½° lies in the first quadrant.

Therefore, sin 22½° is positive.

For all values of the angle A we know that, cos A = 1 - 2 sin2 A2

⇒ 1 - cos A = 2 sin2 A2

⇒ 2 sin2 A2 = 1 - cos A

⇒ 2 sin2 22½˚ = 1 - cos 45°

⇒ sin2 22½˚ = 1−cos45°2

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

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

⇒ sin 22½˚ = 2√−122√−−−−√

⇒ sin 22½˚ = 122−2–√−−−−−−√

Therefore, sin 22½˚ = 122−2–√−−−−−−√