SOLUTION: Let cos beta =a .Find the expression for cos 2beta and sin 2beta in terms of a and hence confirm that - cos(square)2beta + sin(square)2beta = 1

Algebra ->  Algebra  -> Pythagorean-theorem -> SOLUTION: Let cos beta =a .Find the expression for cos 2beta and sin 2beta in terms of a and hence confirm that - cos(square)2beta + sin(square)2beta = 1      Log On

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 Geometry: Pythagorean theorem Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Pythagorean-theorem Question 148438: Let cos beta =a .Find the expression for cos 2beta and sin 2beta in terms of a and hence confirm that - cos(square)2beta + sin(square)2beta = 1Answer by stanbon(57246)   (Show Source): You can put this solution on YOUR website!Let cos(beta) =a/1; this implies that x = a and r=1 Therefore y = sqrt(1-a^2) Therefore sin(beta)= [sqrt(1-a^2)]/r ------------------------------------- Find the expression for cos(2beta) and sin(2beta) in terms of a: cos(2beta) = cos^2(beta)-sin^2(beta = a^2 - [(1-a^2)/r^2] ------------------------------------ ------ sin(2beta) = 2*sin(beta)*cos(beta) = 2 * sqrt(1-a^2)/r] -------------------------- and hence confirm that - cos^2(2beta) + sin^2(2beta) = 1 ------------------ Subsitute to confirm that statement is true. ==================== Cheers, Stan H.