Calculate the difference cos75-cos15.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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Since the functions are matching, we'll use the identity:

cos a - cos b = 2 sin [(a+b)/2]*sin [(b-a)/2]

a = 75 and b = 15

cos 75 - cos 15 = 2 sin [(75+15)/2]*sin[(15-75)/2]

cos 75 - cos 15 = 2 sin 45*sin(-30)

Since the sine function is odd, then sin(-30) = -sin 30

cos 75 - cos 15 = -2 (sqrt2/2)*(1/2)

cos 75 - cos 15 = - (sqrt2/2)

The requested difference is: cos 75 - cos 15 = - (sqrt2/2).

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