if `alpha=(-1+sqrt(-3))/2 , beta=(-1-sqrt(-3))/2` then prove that `alpha/beta+beta/alpha +1=0`

If cosalpha=1/(sqrt(2)),sinbeta=1/(sqrt(3)) , show that tan((alpha+beta)/2)cot((alpha-beta)/2)=5+2sqrt6 or 5-2sqrt6

Given that sin alpha = (sqrt(3))/(2) and cos beta = 0 , then the value of beta - alpha is

If alpha , beta are the roots of x^2 +x+1=0 then alpha beta + beta alpha =

Let (sqrt(2)sin alpha)/sqrt(1+cos 2alpha)=1/7 and sqrt((1-cos2 beta)/2)=1/sqrt(10) where alpha,beta in (0,pi/2) . Then tan(alpha+2beta) is equal to

If : sin (alpha + beta)=1 and sin (alpha-beta)=(1)/(2), "then" : tan (alpha+2beta)*tan(2alpha+beta)=

If alpha and beta are zeroes of a quadratic polynomial ax^(2)+bx+c . Find the value of: (i) alpha^(2)-beta^(2) (ii) alpha^(3)+beta^(3) (iii) alpha^(4)beta+beta^(4)alpha (iv) sqrt((alpha)/(beta))+sqrt((beta)/(alpha)) (v) (alpha^(2))/(beta)+(beta^(2))/(alpha) (alpha^(-1)+(1)/(alpha^(-1)))(beta^(-1)+(1)/(beta^(-1)))

If sqrt2(sin alpha)/(sqrt(1+cos2 alpha))=1/7 and sqrt((1-cos2beta)/2)=1/(sqrt(10)) alpha, beta in (0, pi/2) then tan (alpha + 2 beta) is equal to _________

If tan ""(alpha )/(2) = sqrt ({(1 -e)/( 1 +e)}) tan ""(beta)/(2), Prove that cos beta = ( cos alpha - e )/( 1 - e cos alpha ).

If tan beta = 3 tan alpha, prove that tan (alpha + beta) = (2sin 2beta)/(1+cos 2beta)

If alpha and beta are the roots of x^(2)+4x+6=0 and N=1/((alpha)/(beta)+(beta)/(alpha)) then N=