If `(cos^4alpha)/(cos^2beta)+(sin^4alpha)/(sin^2beta)=1` prove that (i) `sin^4alpha+sin^4beta=2sin^2alphasin^2beta` (ii) `(cos^4beta)/(cos^2alpha)+(sin^4beta)/(sin^2alpha)=1`

Explanation

To prove the given statements, we start with the equation:

\[ \frac{\cos^4 \alpha}{\cos^2 \beta} + \frac{\sin^4 \alpha}{\sin^2 \beta} = 1 \]

### Step 1: Rewrite the equation
Multiply both sides of the equation by \(\cos^2 \beta \sin^2 \beta\):
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