`2tan^(-1){tan.(alpha)/2tan(pi/4-beta/2)}" is equal to " alpha,beta,in (0,pi/2)`

Prove that 2tan^(-1)[tan((alpha)/(2)) tan((pi)/(4)-(beta)/(2))]=tan^(-1)((sin alpha cos beta)/(cos alpha+sin beta))

Show taht 2tan ^ (- 1) (tan ((alpha) / (2)) tan ((pi) / (4) - (beta) / (2))) = tan ^ (- 1) ((sin alpha cos beta) / (cos alpha + sin beta))

If (sec^(4)alpha)/(sec^(2)beta)-(tan^(4)alpha)/(tan^(2)beta)=1 where alpha,betane(pi)/(2) , then find the value of (sec^(4)beta)/(sec^(2)alpha)-(tan^(4)beta)/(tan^(2)alpha)

If tan(alpha-beta)=(sin2 beta)/(3-cos2 beta), then ( i )tan(alpha)=2tan(beta)( ii) (1)/(2)tan(alpha)=tan(beta)( (ii) 2tan(alpha)=3tan(beta)( iv) 3tan(alpha)=2tan(beta)

If tan^(2)alpha tan^(2)beta+tan^(2)beta tan^(2)gamma+tan^(2)gamma tan^(2)alpha+2tan^(2)alpha tan^(2)beta tan^(2)gamma= 1 .(where alpha,beta,gamma in R-{(n pi)/(2)},n in I ) Value of cos2alpha+cos2 beta+cos2gamma is equal to -

If sin(alpha+beta)=1,sin(alpha-beta)=(1)/(2) where alpha,beta in[0,(pi)/(2)], then tan(alpha+2 beta)tan(2 alpha+beta) is equal to