SOLUTION: Prove using trig identities cos3x=cos^3(x)-3sin^2(x)cos(x) Thank you!

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Question 1151362: Prove using trig identities
cos3x=cos^3(x)-3sin^2(x)cos(x)
Thank you!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

cos%283x%29=cos%5E3%28x%29-3sin%5E2%28x%29cos%28x%29

use identity: cos%28alpha+%2B+beta%29+=+cos%28alpha%29+cos%28beta%29-+sin%28alpha%29+sin%28beta%29

write cos%283x%29 as cos%282x%2Bx%29 which is equal to cos%282x%29+cos%28x%29+-+sin%282x%29+sin%28x%29

cos%283x%29=cos%282x%29+cos%28x%29+-+sin%282x%29+sin%28x%29..........since cos%282x%29=cos%28x%2Bx%29=cos%28x%29+cos%28x%29+-+sin%28x%29+sin%28x%29 and sin%282x%29=2+sin%28x%29+cos%28x%29 we have




cos%283x%29=cos%5E3%28x%29++-+sin%5E2%28x%29+cos%28x%29+-2+sin%5E2%28x%29+cos%28x%29%29

cos%283x%29=cos%5E3%28x%29++-+3sin%5E2%28x%29%2A+cos%28x%29+