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Thread: Verifying Identities

  1. #1
    Member purplec16's Avatar
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    Verifying Identities

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

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

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

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

    Also correct.

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

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

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


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

    $\displaystyle \color{red} = 1^2$

    $\displaystyle \color{red} = 1$.


    Is this right so far?
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