- #1

sahilmm15

- 100

- 27

- Homework Statement:
- Given, if ##{\frac{ax}{cos\theta}} + {\frac{by}{sin\theta}} = a^2-b^2## and ##{\frac{axsin\theta}{cos^2\theta}} - {\frac{bycos\theta}{sin^2\theta}} = 0## find the value of ## (ax){^\frac{2}{3}} + (by){^\frac{2}{3}}##

- Relevant Equations:
- N/A, can be done through general algebraic techniques.

I was trying this problem from some 2 hours but unable to crack it. I cannot proceed after few lines i.e$${\frac{axsin\theta}{cos^2\theta}} - {\frac{bycos\theta}{sin^2\theta}} = 0$$ $${\frac{axsin\theta}{cos^2\theta}} = {\frac{bycos\theta}{sin^2\theta}}$$ $${\frac{ax}{by}} ={\frac{cos^3\theta}{sin^3\theta}}$$ at last $$cot\theta = {\frac {ax^\frac{1}{3}} {by^\frac{1}{3}}}$$ This is all what I am able to do.