SOLUTION: Verify the identity using multiple-angle formulas. 1a) cos^(2)3x-sin^(2)3x=cos6x 1b) (sin^(2)2α)/(sin^(2)α)=4-4sin^(2)α

Question 148843: Verify the identity using multiple-angle formulas.

1a) cos^(2)3x-sin^(2)3x=cos6x

1b) (sin^(2)2α)/(sin^(2)α)=4-4sin^(2)α
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
cos^2(3x) - sin^2(3x) = cos(6x)
cos^2(3x) - sin^2(3x) = cos(3x + 3x)
cos^2(3x) - sin^2(3x) = cos(3x)cos(3x) - sin(3x)sin(3x)
~
sin^2(2α) / sin^2(α) = 4 - 4sin^2(α)
sin(2α)sin(2α) / sin^2(α) = 4 - 4sin^2(α)
2sin(α)cos(α)2sin(α)cos(α) / sin^2(α) = 4 - 4sin^2(α)
4cos^2(α) = 4 - 4sin^2(α)
4(1 - sin^2(α)) = 4 - 4sin^2(α)
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SOLUTION: Verify the identity using multiple-angle formulas. 1a) cos^(2)3x-sin^(2)3x=cos6x 1b) (sin^(2)2&#945;)/(sin^(2)&#945;)=4-4sin^(2)&#945;

SOLUTION: Verify the identity using multiple-angle formulas. 1a) cos^(2)3x-sin^(2)3x=cos6x 1b) (sin^(2)2α)/(sin^(2)α)=4-4sin^(2)α