if ` cos ^(-1 ) ""(x )/(a) + cos ^(-1 )""(y)/(b ) = alpha ` prove that ,
` (x^(2) )/(a^(2)) -(2xy)/(ab ) ""cos alpha +(y^(2))/(b^(2))= sin ^(2) alpha `

If tan^(-1)sqrt((a^(2)-x^(2))/(a^(2)+x^(2)) + tan^(-1)sqrt((b^(2)-y^(2))/(b^(2)+y^(2)) = (alpha)/(2) , then show that, (x^(4))/(a^(4))-2(x^(2)y^(2))/(a^(2)b^(2))cos alpha+(y^(4))/(b^(4))=sin^(2)alpha

If cos^-1 x/a + cos^-1 y/b = alpha , then show x^2/a^2 + y^2/b^2 - (2xy)/ab cos alpha = sin^2 alpha

If cos^(-1)((y)/(b))=log((x)/(n))^(n) , prove that, x^(2)y_(2)+xy_(1)+n^(2)y=0 .

(sin alpha)/(sin 2x) +(cos alpha)/(cos 2x) =2

If cos^(2) theta=(a^(2)-1)/(3) and "tan"^(2) (theta)/(2)= tan^((2)/(3))alpha prove that cos ((2)/(3)) alpha+ sin ^((2)/(3)) alpha=((2)/(a))^((2)/(2))

If tan theta = cos2 alpha tan phi, prove that tan (phi - theta) = (tan^(2) alpha sin 2 phi)/(1+ tan^(2) alpha cos 2 phi)

Prove that (cos alpha - cos beta)^(2) +(sin alpha - sin beta)^(2) = 4 "sin"^(2) (alpha-beta)/2

If x cos alpha +y sin alpha = 4 is tangent to (x^(2))/(25) +(y^(2))/(9) =1 , then the value of alpha is

If tan^(2) alpha = 1 + 2 tan^(2) beta, "prove that ," cos 2 beta = 1 + 2 cos 2 alpha

P( asec alpha, b tan alpha ) and Q (a sec beta, b tan beta) are two given points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1. Show that the equation of the chord PQ is (x)/(a) cos (alpha - beta)/(2) - (y)/(b) sin (alpha + beta)/(2) = cos (alpha+beta)/(2).