Homework SourseWrite the given expression in terms of x and y only sinsin1
Write the given expression in terms of x and y only. sin(sin^-1 (x) + cos^-1 (y)) x + y squareroot 1 - x^2/squareroot 1 + y^2![Write the given expression in terms of x and y only. sin(sin^-1 (x) + cos^-1 (y)) x + y squareroot 1 - x^2/squareroot 1 + y^2Solutionsin[sin^-1(x) + cos^-1(y)]](/WebImages/28/write-the-given-expression-in-terms-of-x-and-y-only-sinsin1-1077807-1761565573-0.webp "Write the given expression in terms of x and y only. sin(sin^-1 (x) + cos^-1 (y)) x + y squareroot 1 - x^2/squareroot 1 + y^2Solutionsin[sin^-1(x) + cos^-1(y)]")
Solution
sin[sin^-1(x) + cos^-1(y)]
Let a = sin^-1(x) ; b = cos^-1(y)
x = sina ; cosa = sqrt( 1- x^2) ; cosb =y ; sinb = sqrt(1 - y^2)
sin(a+ b) = sinacosb + cosasinb
= x(y) + sqrt(1-x^2)(sqrt( 1-y^2)
= xy + sqrt[(1-x^2)(1 - y^2)
sin[sin^-1(x) + cos^-1(y)] =
