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8. Solve this need urgently​

Answer»

Step-by-step EXPLANATION:

\text{x = a sin Z}\\\text{a = }\frac{\text{x}}{\text{sin Z}}\\\\\text{y = b cos Z}\\\text{b = }\frac{\text{y}}{\text{cos Z}}\\\\\boxed{\text{To prove that: }\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1}\\\\\\\text{LHS: }\frac{\text{(a sin Z)}^2 \text{ x (sin Z)}^2}{\text{(a sin Z)}^2} + \frac{\text{(b cos Z)}^2 \text{ x (cos Z)}^2}{\text{(b cos Z)}^2}\\\\

= \frac{\text{a}^2 \text{sin}^2 \text{Z} \text{ x sin}^2 \text{Z}}{\text{a}^2 \text{sin}^2 \text{Z}} + \frac{\text{b}^2 \text{cos}^2 \text{Z} \text{ x cos}^2 \text{Z}}{\text{b}^2 \text{cos}^2 \text{Z}}\\\\= \text{sin}^2\text{ Z} + \text{cos}^2\text{ Z}\\\\= 1 \\\\\boxed{\text{Hence Proved.}}

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