यदि `cos^(-1)""(x)/(a) + cos^(-1)""(y)/(b) =alpha`
सिद्ध करे कि `(x^(2))/(a^(2))-(2xy)/(ab) (cos alpha) + (y^(2))/(b^(2)) = sin^(2)alpha`

Explanation

दिया है, `cos^(-1) ""(x)/(a) +cos^(-1)""(y)/(b) =alpha`
`rArr cos^(-1)[(x)/(a)*(y)/(b)-sqrt(1-(x^(2))/(a^(2)))sqrt(1-(y^(2))/(b^(2)))] = alpha`
`rArr (x)/(a)*(y)/(b) -sqrt(1-(x^(2))/(a^(2)))sqrt(1-(y^(2))/(b^(2))) = cos alpha`
`rArr [(x)/(a)*(y)/(b) -cos alpha]^(2) = (1-(x^(2))/(a^(2)))(1-(y^(2))/(b^(2)))`
`rArr (x^(2))/(a^(2)) *(y^(2))/(b^(2)) +cos^(2) alpha-(2xy)/(ab) (cos alpha) = 1-(x^(2))/(a^(2))-(y^(2))/(b^(2)) +(x^(2))/(a^(2)) *(y^(2))/(b^(2))`
`rArr (x^(2))/(a^(2)) +(y^(2))/(b^(2)) - (2xy)/(ab) (cos alpha) = 1- cos^(2) alpha`
`rArr (x^(2))/(a^(2)) + (y^(2))/(b^(2)) - (2xy(cos alpha))/(ab) = sin^(2) alpha`