SOLUTION: Using techniques with sum and difference formulas, find any acceptable formula for cos 3(theta) You do not have to fully simplify your answer, but you must at least simplify identi

Algebra ->  Trigonometry-basics -> SOLUTION: Using techniques with sum and difference formulas, find any acceptable formula for cos 3(theta) You do not have to fully simplify your answer, but you must at least simplify identi      Log On


   

Question 981304: Using techniques with sum and difference formulas, find any acceptable formula for cos 3(theta) You do not have to fully simplify your answer, but you must at least simplify identities.
Someone please help me. Thank you.
Found 2 solutions by josgarithmetic, macston:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
cos%283%2Atheta%29=cos%28theta%2B2theta%29
cos%28theta%29cos%282theta%29-sin%28theta%29sin%282theta%29

cos%5E3%28theta%29-cos%28theta%29sin%5E2%28theta%29-2%2Asin%5E2%28theta%29cos%28theta%29

Hard to know at what stage you are finished.

Continuing----

cos%28theta%29%28cos%5E2%28theta%29-sin%5E2%28theta%29-2%2Asin%5E2%28theta%29%29
Using the Pythagorean Identity for cos%5E2%28theta%29,
cos%28theta%29%281-sin%5E2%28theta%29-sin%5E2%28theta%29-2sin%5E2%28theta%29%29
highlight_green%28cos%28theta%29%281-4%2Asin%5E2%28theta%29%29%29------Most interesting because looks simplest.

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
T=theta
.
cos3T = cos(2T+T)...cos(a+b)=cos(a)cos(b)-sin(a)sin(b)
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cos3T = cos2TcosT-sin2TsinT...cos(2a)=cos^2(a)-sin^2(a) and sin(2a)=2sinTcosT
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cos3T = cosT(cos^2T-sin^2T)-sinT(2sinTcosT)
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cos3T = cos^3T-sin^2cosT-2sin^2TcosT
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cos3T = cos^3T-3sin^2TcosT...sin^2(a)=1-cos^2(a)
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cos3T = cos^3T-3(1-cos^2T)(cosT)
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cos3T = cos^3T-3(cosT-cos^3T)
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cos3T = cos^3T+3cos^3T-3cosT
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cos3T = 4cos^3T-3cosT