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 roots of the equation a cos theta + b sin theta = c , then find the value of tan (alpha + beta).

If alpha and beta are 2 distinct roots of equation a cos theta + b sin theta = C then cos( alpha + beta ) =

If alpha and beta are the solution of a cos theta + b sin theta = c , then

If alpha "and " beta be two distinct real numbers such that (alpha-beta) ne 2 n pi for any integer n satisfying the equations a cos theta + b sin theta =c then prove that (i) "cos " (alpha+ beta) =(a^(2) -b^(2))/(a^(2) +b^(2)) " "(ii) "sin " (alpha + beta) = (2ab)/(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 and beta are the two different roots of equations a cos theta+b sin theta=c , prove that (a) tan (alpha+beta)=(2ab)/(a^(2)-b^(2)) (b) cos(alpha+beta)=(a^(2)-b^(2))/(a^(2)+b^(2))

If alpha and beta are distinct roots of acostheta+b sintheta=c , prove that sin(alpha+beta)=(2a b)/(a^2+b^2)

If alpha, beta are roots of the equation 2x^2 + 6x + b = 0 (b < 0), then alpha/beta+beta/alpha is less than

If sin alpha + sin beta = a and cos alpha + cos beta = b, prove that : cos (alpha-beta) = 1/2 (a^2 + b^2 -2)

If alpha,beta are the roots of the equation ax^(2)-bx+b=0 , prove that sqrt((alpha)/(beta))+sqrt((beta)/(alpha))-sqrt((b)/(a))=0 .