If `alpha and beta` be two roots of the equation `a cos theta+ b sin theta=c`, show that `sin alpha+ sin beta=(2bc)/(a^(2)+b^(2)) ,sin alpha sin beta =(c^(2)-a^(2))/(a^(2)+b^(2)) and tan (alpha+ beta)=(2ab)/(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, beta (alpha ne beta) satisfy the equation a cos theta + b sin theta=c then the value of tan ""(alpha + beta)/(2) is-

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 cos alpha+ cos beta= a and sin alpha+ sin beta =b , then show that sin 2 alpha+ sin 2 beta =2 ab(1- (2)/(a^(2)+ b^(2))) .

Prove that (cos alpha - cos beta)^(2) +(sin alpha - sin beta)^(2) = 4 "sin"^(2) (alpha-beta)/2

In sin alpha+ sin beta=(1)/(2) and cos alpha+ cos beta =(5)/(4) , find the value of tan alpha+tan beta .

Prove that (cos2 alpha-cos 2 beta)/(sin2 alpha+sin2 beta)=tan(beta-alpha)

sin alpha + sin beta = a "and" cos alpha + cos beta = b sin (alpha + beta) =

If tan (alpha + beta) = a + b " and " tan ( alpha -beta) = a-b, "then show that, " a tan alpha - b tan beta = a^(2)-b^(2)

If a cos theta+ b sin theta= c then find the quadratic equation whose root are sin^(2) alpha and sin^(2) beta