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Solution

1) cos195 = cos(45 + 150)

We use this: cos(A + B) = cosAcosB - sinAsinB
Let A = 45 and B = 150
cos(45 + 150) = cos45cos150 - sin45sin150

cos(45 + 150) = sqrt[2]/2 * -sqrt[3]/2 - sqrt[2]/2 * 1/2

cos(45 + 150) = (-sqrt[6] - sqrt[2])/4
So, the exact value of cos195 degrees is (-sqrt[6] - sqrt[2])/4