[" 8.If "cos^(-1)x+cos^(-1)y=theta" ,then prove that: "],[qquad sin^(-1)x+sin^(-1)y=pi-theta]

If cos^(-1)x+cos^(-1)y=pi/2 then prove that cos^(-1)x=sin^(-1)y

If cos^(-1)x+cos^(-1)y=theta show that x^(2)-2xy cos theta+y^(2)=sin^(2)theta

If cos^-1 x+cos^-1 y=theta , prove that x^2+y^2-2xycostheta=sin^2theta

If sin ^ (- 1) x + sin ^ (- 1) y = (pi) / (2), then prove that sin ^ (- 1) x = cos ^ (- 1) y

If sin(pi cos theta)=cos(pi sin theta) ,then prove that : theta=(1)/(2)sin^(-1)(3/4)

If "cos"^(-1)(x/y) +"cos"^-1(y/3)= theta, "prove that" 9x^2- 12xy "cos" theta +4y^2 =36 "sin"^2 theta .

If x=a(1-cos theta),y=a(theta+sin theta), prove that (d^(2)y)/(dx^(2))=-(1)/(a) at theta=(pi)/(2)

If x=a(1+cos theta),y=a(theta+sin theta), prove that (d^(2)y)/(dx^(2))=(-1)/(a) at theta=(pi)/(2)

If quad sin (theta + (7 pi) / (12)) + sin (theta- (pi) / (12)) + sin (theta + (3 pi) / (12)), Y = cos (theta + (7 pi) / (12)) + cos (theta- (pi) / (12)) + cos (theta + (3 pi) / (12)) then prove that (X) / (Y) - (Y) / (X) = 2tan2 theta

If x=(2sin theta)/(1+cos theta+sin theta), then prove that (1-cos theta+sin theta)/(1+sin theta) is equal to x