SOLUTION: Let cos beta =a .Find the expression for cos 2beta and sin 2beta in terms of a and hence confirm that

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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 = 1
Answer by stanbon(75887) (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
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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]
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and hence confirm that - cos^2(2beta) + sin^2(2beta) = 1
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Subsitute to confirm that statement is true.
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Cheers,
Stan H.

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