Show taht `2tan^-1(tan(alpha/2)tan(pi/4-beta/2))=tan^-1((sinalphacosbeta)/(cosalpha+sinbeta))`

Prove that: tan(alpha+beta)tan(alpha-beta)=(sin^2 alpha-sin^2 beta)/(cos^2 alpha-sin^2 beta)

Show by vector method that sin(alpha-beta)=sinalphacosbeta-cosalpha sinbeta.

Show that (tan^-1)(2ab)/(a^2-b^2)+(tan^-1)(2xy)/(x^2-y^2)=(tan^-1) (2alphabeta)/(alpha^2-beta^2), where alpha=ax- by and beta=ay+bx.

Show that 2tan^-1 (-3)=-pi/2+tan^-1(-4/3)

Show that 2tan^-1 (-3)=-pi/2+tan^-1(-4/3)

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

show that tan^(-1)(1/2)+tan^(-1)(2/11)=tan^(-1)(3/4)

If alpha+beta+gamma=2pi, then (a) tan(alpha/2)+tan(beta/2)+tan(gamma/2)=tan(alpha/2)tan(beta/2)tan(gamma/2) (b) tan(alpha/2)tan(beta/2)+tan(beta/2)tan(gamma/2)+tan(gamma/2)tan(alpha/2)=1 (c) tan(alpha/2)+tan(beta/2)+tan(gamma/2)=-tan(alpha/2)tan(beta/2)tan(gamma/2) (d)none of these

Sum the series tan alpha tan (alpha+beta)+tan(alpha+beta)+tan(alpha+2beta)+tan(alpha+2beta)tan(alpha+3beta)+… to n terms

If tan beta=cos theta tan alpha , then prove that tan^(2)""(theta)/(2)=(sin(alpha-beta))/(sin(alpha+beta)) .