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Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

Double angle formula is can be derived using the sum of angle formulas like cos( x + y) = cos x * cos y - sin x * sin y what if x = y , then all y substitute x then equation becomes cos 2x = cos^2 x - sin^2 x and cos 2x is what you called double angle then manipulate the equation using trigo identities the pythagorian theorem cos^2 x = 1 - sin^2 x substitute to the equation so then you come to equation cos 2x = (1 - sin^2 x ) - sin^2 x ; combine like terms cos 2x = 1 - 2sin^2x

then for your problem choose what answer do you want or the best if two equation will you give to your teacher for your home work if this is a home work haha lets back to your equation cos ^2 75 - sin^2 75 is equal either cos 2(75) or 1 - 2 sin^2 (75) or 2cos^2 (75) - 1 either of those is equal to - sqroot(3)/2 or just - 0.8660