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If cos^2alpha-sin^2alpha=tan^2beta," the...

If `cos^2alpha-sin^2alpha=tan^2beta," then prove that "tan^2alpha=cos^2beta-sin^2beta`.

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To prove that if \( \cos^2 \alpha - \sin^2 \alpha = \tan^2 \beta \), then \( \tan^2 \alpha = \cos^2 \beta - \sin^2 \beta \), we can follow these steps: ### Step 1: Start with the given equation We have: \[ \cos^2 \alpha - \sin^2 \alpha = \tan^2 \beta \] ...
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(cos^2alpha-cos^2beta)/(cos^2alpha cos^2beta)=tan^2beta-tan^2alpha