Minimum value of `(sec^4alpha)/(tan^2beta)+(sec^4beta)/(tan^2alpha),` where `alpha!=pi/2,beta!=pi/2`,0

Prove that (sec^4alpha)/(tan^2beta)+(sec^4beta)/(tan^2alpha)ge8 . If each term in the expression is well defined.

If alpha and beta are the roots of the equation 3x^(2) - 5x + 2 = 0 , find the value of (i) (alpha)/(beta) + (beta)/(alpha) (ii) alpha-beta (iii) (alpha^(2))/(beta) + (beta^(2))/(alpha)

Find the value of x such that ((x+alpha)^2-(x+beta)^2)/(alpha+beta)=(sin (2theta))/(sin^2 theta) , where alpha and beta are the roots of the equation t^2-2t+2=0 .

The minimum value of the expression sin alpha + sin beta+ sin gamma , where alpha,beta,gamma are real numbers satisfying alpha+beta+gamma=pi is

If sec alpha is the average of sec(alpha - 2beta) and sec(alpha + 2beta) then the value of (2 sin^2 beta - sin^2 alpha ) where beta!= n pi is

If cosx-sinalphacotbetasinx=cosa , then the value of tan(x/2) is -tan(alpha/2)cot(beta/2) (b) tan(alpha/2)tan(beta/2) -cot((alphabeta)/2)tan(beta/2) (d) cot(alpha/2)cot(beta/2)

If (cos^(4)alpha)/(cos^(2) beta) + (sin^(4)alpha)/(sin^(2)beta) = 1, prove that (cos^(4)beta)/(cos^(2) alpha) + (sin^(4)beta)/(sin^(2)alpha)= 1

If alpha+beta=pi/2a n dbeta+gamma=alpha, then tanalpha equals

If 2 sin 2alpha=tan beta,alpha,beta, in((pi)/(2),pi) , then the value of alpha+beta is