Use a right triangle to write the following expression as an

Use a right triangle to write the following expression as an algebraic expression. Cos (sin^-1 9/x) cos (sin-1 9/x) = (Type an exact answer, using radicals as needed.)

Solution

cos( sin^-1(9/x) )

Let sin^-1(9/x) =y

siny = 9/x

Its right angled triangle so, Base = sqrt( x^2 -81)

So cosy = sqrt(x^2 -81) /x ---->y= cos^-1(sqrt(x^2 -81) /x)

cos( sin^-1(9/x) ) = cosy = cos{cos^-1(sqrt(x^2 -81) /x)}

= sqrt( x^2 -81)/x