what is the value of sin 221/2 degrees
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Step-by-step explanation:
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–√−−−−−−√
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