How do you use a half-angle formula to find cos (pi/8)?

We have to find the value of cos (π/8)

Solution

cos π= 180

cos(π/8) = 180/8

cos(π/8) = 22.5

We can solv using double identity formula

cos 2A = cos2A – sin2A
cos2A = cos2A – (1 – cos2A) = 2cos2A – 1
cos 45° = 2cos2 22.5° – 1
√2/2 + 1 = 2cos2 22.5
√2/4 + 1/2 = cos2 22.5°
cos 22.5° = √[ (√2 + 2)/4]= √(√2 + 2) /2

cos (π/8)= √[ (√2 + 2)/4]= √(√2 + 2) /2

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