Give me each & every step of solution with reason .. Question is fully in attachment it is about to prove (ax)^2/3+(by)^2/3=(a^2-b^2)^2/3

From 2nd eq in question...-> ax sinß / cos²ß = by cosß / sin²ß…-> tan³ß = by / ax-> tanß = (by/ax)⅓...From tanß you can take out sinß and cos ß which are respectively:::: sinß = (by)⅓ / sqroot of [ (by)⅔ + (ax)⅔ ]…cosß = (ax)⅓ / sqroot of [ (by)⅔ + (ax)⅔ ]…Putiimg this in 1st eq in the question....-> [ ax/ (ax)⅓ + by/ (by)⅓ ]*[sqroot of [ (by)⅔ + (ax)⅔ ] ] = a² - b².....-> [ (by)⅔ + (ax)⅔ ]⅔ = a² - b²....-> (by)⅔ + (ax)⅔ = ( a² - b ) ^ 3/2....Hence proved...

Correction for the last step::-> [ (by)⅔ + (ax)⅔ ] ^3/2( instead of 2/3 wrongly printed ) = a² - b²....-> (by)⅔ + (ax)⅔ = ( a² - b ) ^ 2/3......Hence proved...