If `alpha, beta` are the solutions of the equation
`a tantheta+b sectheta=c` then show that `tan(alpha+beta)=(2ac)/(a^2-c^2`.

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 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,beta are the roots of the quadratic equation ax^2+bx+c=0 and 3b^2=16ac then

If the roots of the equation ax^2+bx+c=0 are alpha , beta and the roots of the equation Ax^2+Bx+C=0 are (alpha+delta) and (beta+delta) then show that (b^2-4ac)/a^2=(B^2-4AC)/A^2

If the roots of the equation ax^2+bx+c=0 are alpha and beta then show that 1/(a alpha+b)+1/(abeta+b)=b/(ac) .

If alpha, beta are the roots of the quadratic equation ax^(2)+bx+c=0 and 3b^(2)=16 ac then

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 the roots of the equation ax^(2)+bx+c=0 , then show that underset(xrarralpha)"lim"(1-cos(ax^(2)+bx+c))/((x-alpha)^(2))=(a^(2))/(2)(alpha-beta)^(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 tan(alpha+beta)=a+b and tan(alpha-beta)=a-b then show that atanalpha-btanbeta=a^2-b^2