Let `alpha, beta` be non-zero real numbers such that `2(cosbeta-cosalpha) +cosalphacosbeta = 1`. Then which of the following is/are true ?

Let alphaa n dbeta be nonzero real numbers such that 2(cosbeta-cosalpha)+cosalphacosbeta=1 . Then which of the following is/are true? sqrt(3)tan(alpha/2)+tan(beta/2)=0 sqrt(3)tan(alpha/2)-tan(beta/2)=0 t a n""(alpha/2)+sqrt(3)tan(beta/2)=0 t a n""(alpha/2)-sqrt(3)tan(beta/2)=0

If alpha and beta are non-zero real number such that 2(cos beta-cos alpha)+cos alpha cos beta=1. Then which of the following is treu?

f(alpha,beta) = cos^2(alpha)+ cos^2(alpha+beta)- 2 cosalpha cosbeta cos(alpha+beta) is

"Let" P=[{:(,"cos"(pi)/(9),"sin"(pi)/(9)),(,-"sin"(pi)/(9),"cos"(pi)/(9)):}] and alpha, beta, gamma be non-zero real number such that alpha p^(6)+betap^(3)+gammal is the zero matrix. Then find the value fo (alpha^(2)+beta^(2)+gamma^(2))^(alpha-betaxxbeta-gammaxxgamma-alpha)

Let alpha and beta be two real roots of the equation 5cot^2x-3cotx-1=0 , then cot^2 (alpha+beta) =

Prove that |cosalpha-cosbeta|lt=|alpha-beta|

Let alpha and beta be two distinct complex numbers, such that abs(alpha)=abs(beta) . If real part of alpha is positive and imaginary part of beta is negative, then the complex number (alpha+beta)//(alpha-beta) may be

Let f(x)=sin^(2)(x +alpha)+sin^(2)(x +beta)-2cos(alpha-beta)sin(x+alpha)sin(x +beta) . Which of the following is TRUE ?

If (cosalpha)/(sinbeta)=n and (cosalpha)/(cosbeta)=m , then find cos^(2)beta ?

Q. Let p and q real number such that p!= 0 , p^2!=q and p^2!=-q . if alpha and beta are non-zero complex number satisfying alpha+beta=-p and alpha^3+beta^3=q , then a quadratic equation having alpha/beta and beta/alpha as its roots is