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

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

Prove that : 2tan^(-1)[tan prop//2 tan beta//2]=cos^(-1)[(cos prop +cosbeta)/(1+cosalpha cos beta)]

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

if tan alpha=2tan beta show that (sin(alpha+beta))/(sin(alpha-beta))=3

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

If tan^(2)alpha=1+2tan^(2)beta , then sqrt(2)cosalpha-cosbeta=?

if 3tan alpha=4tan beta then prove that tan(alpha-beta)=(tan beta)/(4tan^(2)beta+3)=(sin beta*cos beta)/(3+sin^(2)beta)

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

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