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
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Question 148843
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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
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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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