Question

solve it

x/acos¢ + y/bsin¢ and ax/cos¢ -by/sin¢ = a²+ b² then proove that
x²/a² +y²/b² = 1

Answer 1

Hey !!!

solution :- x/acos¢ = y/bsin¢ = k [suppose]

then, x = akcos¢ -----1) and y = bksin¢ -----2)

again , ax/cos¢ -by/sin¢ = a² -b²

•°• a×akcos¢ /cos¢ - b×bksin¢/sin¢ = a² - b²

by putting the value of x and y we get .

=> a²k - b²k = a² - b²

=> k(a² -b² ) = a² -b²

•°• from (1) x = acos¢

=> x² = a²cos²¢

=> x²/a² = cos²¢

AND then from 2 ) y = bsin¢

=> y² = b²sin²¢ --------4)

=> y²/b² = sin²¢ --------5)

adding 4 and 5 equation

x²/a² + y²/b² = cos²¢ + sin²¢

x² /a² + y²/b² = 1 prooved

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Hope it helps you !!!

@Rajukumar111