If `alpha and beta` satisfy the equation `a cos 2x + b sin 2x = c` then prove that (i) `cos^2alpha+cos^2beta=(a^2+ac+b^2)/(a^2+b^2) ` (ii) `cosalpha*cosbeta=(a+c)/(2sqrt(a^2+b^2))`

If alpha\ &\ beta satisfy the equation, a cos2theta+b sin2theta=c then prove that : cos^2alpha+cos^2beta=(a^2+a c+b^2)/(a^2+b^2)

If alpha, beta are the roots of the equation a cos theta + b sin theta = c , then prove that cos(alpha + beta) = (a^2 - b^2)/(a^2+b^2) .

If alpha and beta are two real numbers satisfying the equation a cos x + b sin x = c , prove that : sin (alpha+ beta)= (2ab)/(a^2+b^2) .

If alpha and beta are two real numbers satisfying the equation a cos x + b sin x = c, prove that : tan (alpha+ beta)= (2ab)/(a^2-b^2) .

If alpha and beta are the solutions of a cos theta+b sin theta=c , then prove that : cos (alpha- beta)= (2c^2- (a^2+b^2))/(a^2+b^2) .

If alpha,beta are the roots of the equation a cos theta+b sin theta=c, then prove that cos(alpha+beta)=(a^(2)-b^(2))/(a^(2)+b^(2))

If" " alpha " and " beta " satisfy the equation " a cos 2 theta + b sin 2 theta = c " then show that " cos^(2) alpha + cos ^(2)beta =1 + (ac)/(a^(2) + b^(2))

If alpha and beta are roots of the equation acostheta+bsintheta=c then prove that, cosalpha+cosbeta=(2ac)/(a^(2)+b^(2))andcosalpha.cosbeta=(c^(2)-b^(2))/(a^(2)+b^(2))

If angles alpha and beta satisfy the equation a cos theta+ b sin theta= c(a,b,c are constants), prove that- (a) sin (alpha+ beta)= (2ab)/(a^(2)+b^(2)) (b) cos (alpha+beta)=(a^(2)-b^(2))/(a^(2)+b^(2)) (c) cos (alpha- beta)=(2c^(2)-(a^(2)+b^(2)))/(a^(2)+b^(2))

If alpha and beta are the solution of the equation a cos2 theta+b sin2 theta=c then cos^(2)alpha+cos^(2)beta is equal to