Using mean value theorem, show that `(beta-alpha)/(1+beta^2) < tan^(-1)beta-tan^(-1)alpha < (beta-alpha) (1+alpha^2) , beta > alpha > 0.`

Show by using mean value theorem and taking f(x)=log x, that 1-(alpha)/(beta)

If sin beta = 1/5 sin(2alpha +beta) , show that tan(alpha +beta) = 3/2 tan alpha .

If alpha, beta are zeroes of polynomial 6x^(2) +x-1 , then find the value of (i) alpha^(3) beta + alpha beta^(3) , (ii) alpha/beta + beta/alpha +2(1/alpha + 1/beta) + 3 alpha beta

If alpha,beta, are roots of the equation x^(2)+sqrt(x)alpha+beta=0,beta beta then values of alpha and beta are 1. alpha=1 and beta=12 .alpha=1 and beta=-2 3.alpha=2 and beta=1alpha=2 and beta=-2

Find the value of, cos alpha cos beta, cos alpha sin beta, -no alpha-sin beta, cos beta, 0 sin alpha cos beta, sin alpha sin beta, cos alpha] |

If alpha and beta be the roots of equation x^(2) + 3x + 1 = 0 then the value of ((alpha)/(1 + beta))^(2) + ((beta)/(1 + alpha))^(2) is equal to

If alpha and beta are roots of the quadratic polynomial f(x)=px^(2)+qx+r ;then find the value of (i) alpha^(2)+beta^(2)( ii) (alpha)/(beta)+(beta)/(alpha) (iii) (1)/(alpha^(3))+(1)/(beta^(3))( iv )(alpha^(2))/(beta)+(beta^(2))/(alpha)

If sin alpha+sin beta=a and cos alpha+cos beta=b show that sin(alpha+beta)=(2ab)/(alpha^(2)+beta^(2))

(i) If alpha,beta be the imaginary cube root of unity, then show that alpha^(4)+beta^(4)+alpha^(-1)beta^(-1)=0