How do you find the exact values of cos 22.5 degrees using the half-angle formula?

The half-angle formula for cos is cos x/2 = ± √ (1 + cosx) / 2. 

Answer: The exact value of cos 22.5 degrees is 0.92387953...

Lets us see the solution.

Explanation:

⇒ cos (22.5º) = cos (45º/2)

⇒ cos² (45º/2) = [1 + cos 45º] / 2

⇒ cos² (45º/2) = (1 + √2/2) / 2

⇒ cos² (45º/2) = [(2 + √2) / 2] / 2

⇒ cos (45º/2) = √ [(2 + √2) / 4]

⇒ cos (45º/2) = 1/2 √ (2+√2)

√ (2 + √2) = 1.84775906...

⇒ cos (45º/2) = 1.84775906.../ 2 = 0.92387953...

Thus, the exact value of cos 22.5 degrees is 0.92387953...