How do you find the exact values of cos22.5° using the half-angle formula?
Compute the required value.
We know that, cosA=cos2A2-sin2A2
Here A=45°
⇒ cosA=cos2A2-1-cos2A2
⇒ cosA=2cos2A2-1
⇒ cos45°=2cos222.5°-1
⇒ 12+1=2cos222.5° cos45°=12
⇒ 22+1=2cos222.5°
⇒ 2+24=cos222.5°
⇒ cos22.5°=(2+2)2
⇒ cos22.5°≈0.92
Hence, the exact value of cos22.5° is (2+2)2 or 0.92.
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