Posted by **kk** on Monday, April 2, 2012 at 12:47pm.

2cos^2 22.5-1 (find exact value)

- trig -
**Steve**, Monday, April 2, 2012 at 1:20pm
cos^2 θ/2 = (1 + cosθ)/2

cos^2 22.5° = (1 + cos 45°)/2

= (1 + √2/2)/2

= (2 + √2)/4

- trig -
**Steve**, Monday, April 2, 2012 at 1:37pm
hmmph

It would help to notice that

2cos^2 θ - 1 = cos 2θ

so what you have is just cos 45° = 1/√2

note that 2(2+√2)/4 - 1 = 1+√2/2-1 = √2/2 = 1/√2

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