Verified answer

you can do this many ways. i am doing it by splitting 75 degrees into 45degrees and 30 degrees.

cos(75)=cos(45+30)

recall the formula cos(a+b)=cos a cosb-

sin a sin b

cos(45+30)=cos(30)sin(45)-

sin(30)sin(45)

cos(45+30)=((sqrt(3))/2)((sqrt(2))/2)-(0.5)((sqrt(2))/2)

cos(45+30)

=(sqrt(6)- sqrt(2))/4

Cos 75 Degrees

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Look for perfect squares that divide evenly into the number within the radical. Since 25 is the square of 5, split the sqrt(75) into sqrt(25) * sqrt(3): 4 * sqrt(75) = 4 * sqrt(25) * sqrt(3) = 4 * 5 * sqrt(3) = 20 * sqrt(3)