If `cosalpha=x/(y+z)`,`cosbeta=y/(z+x)`and `cosgamma=z/(x+y)`then show that `tan^2(alpha/2)+tan^2(beta/2)+tan^2(gamma/2)=1`

If alpha+ beta=(pi)/(2) and beta+ gamma= alpha then prove that tan alpha=tan beta+2 tan gamma .

If cosalpha+cosbeta=2/3 and sinalpha+sinbeta=2/5 then find the vvalue of tan((alpha+beta)/2)

If cosalpha=siny/sinx , cosbeta=sinz/sinx and cos(alpha-beta)=siny sinz .Show that tan^2x=tan^2y+tan^2z

If cosalpha+cosbeta=1/3 and sinalpha+sinbeta=1/4 ,show that tan ((alpha+beta)/2)=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

If alpha, beta and gamma are angle such that tan alpha + tan beta+tan gamma= tan alpha tan beta tan gammaand x=cos alpha + I sin alpha, y=cos beta+ I sin beta and z= cos gamma+ I sin gamma, then the value of xyz is -

If x cos alpha + y sin alpha=x cos beta+y sin beta,"show that",y=x "tan"(alpha+beta)/2

If cot^(-1)(sqrt(cosalpha))-tan^(-1)(sqrt(cosalpha))=x , then sinx is tan^2alpha/2 (b) cot^2alpha/2 (c) tan^2alpha (d) cotalpha/2

If (tan (alpha- beta+ gamma))/(tan (alpha+ beta- gamma))=(tan beta)/( tan gamma) , show that either sin (beta- gamma)=0 or sin 2 alpha+ sin 2 beta+ sin 2 gamma=0

If alpha!=beta and atanalpha+b tanbeta=(a+b)tan((alpha+beta)/2) ,then show that (cosalpha)/(cosbeta)=a/b