1. ## 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?

2. Originally Posted by purplec16

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

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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