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Math Help - Verifying Identities

  1. #1
    Member purplec16's Avatar
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    Verifying Identities

    (sin^2\theta+cos^2\theta)^3=1
    (sin^2\theta+cos^2\theta)((sin^2\theta)^2+2sin^2\t  heta cos^2\theta+(cos^2\theta)^2)=1
    Is this right so far?
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  2. #2
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    Quote Originally Posted by purplec16 View Post

    (sin^2\theta+cos^2\theta)^3=1

    Correct, since \color{red}\sin^2{\theta} + \cos^2{\theta} = 1. This means \color{red}(\sin^2{\theta} + \cos^2{\theta})^3 = 1^3 = 1.

    (sin^2\theta+cos^2\theta)((sin^2\theta)^2+2sin^2\t  heta cos^2\theta+(cos^2\theta)^2)=1

    Also correct.

    \color{red}(\sin^2{\theta} + \cos^2{\theta})[(\sin^2{\theta})^2 + 2\sin^2{\theta}\cos^2{\theta} + (\cos^2{\theta})^2]

    \color{red} = 1
    [(\sin^2{\theta})^2 + 2\sin^2{\theta}\cos^2{\theta} +  (\cos^2{\theta})^2]

    \color{red} = (\sin^2{\theta})^2 + 2\sin^2{\theta}\cos^2{\theta} +  (\cos^2{\theta})^2


    \color{red} = (\sin^2{\theta} + \cos^2{\theta})^2

    \color{red} = 1^2

    \color{red} = 1.


    Is this right so far?
    ...
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