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Prove that

Posted March 24th, 2008 by alpha
in
$$ tan^3\alpha-sin^2\alpha= tan^3\alpha.sin^2\alpha$$
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Answer

On March 24th, 2008 Structure says:
$$ tan^3\alpha-sin^2\alpha= tan^3\alpha.sin^2\alpha$$

This is false
It is true

$$ \tan^2\alpha-\sin^2\alpha= \tan^2\alpha\sin^2\alpha$$

as

$$ \tan^2\alpha-\tan^2\alpha\sin^2\alpha=\tan^2\alpha(1-\sin^2\alpha)=\tan^2\alpha\cos ^2\alpha=\sin^2\alpha$$

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