Question

if x = a sin & y = b tan ,than prove that a square - b square / x square y square =1​

Answer 1

Solution:-

x = a sin theta : y = b tan theta  ....(Given)

L.H.S. = a²/x² - b²/y² = a²/(a sin theta)² - b²/(b tan theta)²

a² and b² are cancelled and then we get  1/sin² theta - 1/sin² theta/cos² theta

[∴ tan theta = sin theta/cos theta]

1/sin² theta - cos² theta/sin² theta

= (1-cos² theta)/sin² theta  ....[∴ sin² theta + cos² theta = 1]

sin² theta/sin² theta = 1

= R.H.S

⇒ a²/x² - b²/y²

Hence proved.