Given that: `(1+cosalpha)(1+cosbeta)(1+cosgamma)=(1-cosalpha)(1-cosbeta)(1-cosgamma)dot` Show that one of the values of each member of this equality is `sinalphasinbetasingammadot`

Prove that (sinalpha)/(1+cosalpha)+(1+cosalpha)/(sin alpha)=2"cosec "alpha .

If cosalpha=1/2(x+1/x) cosbeta=1/2(y+1/y) then cos(alpha-beta) is equal to

Evaluate: int(1+cosalphacosx)/(cosalpha+cosx) dx

Show that the maximum value of (1/x)^x is e^(1/e)dot

If alpha+beta+gamma=pi , prove that : cos^2 alpha + cos^2 beta + cos^2 gamma+2cosalpha cosbeta cosgamma=1 .

If cosalpha+cosbeta+cosgamma=0 , then prove that cos3alpha+cos3beta+cos3gamma=12cosalphacosbetacosgamma

Statement 1: If cosalpha,cosbeta,a n dcosgamma are the direction cosines of any line segment, then cos^2alpha+cos^2beta+cos^2gamma=1. Statement 2: If cosalpha,cosbeta,a n dcosgamma are the direction cosines of any line segment, then cos2alpha+cos2beta+cos2gamma=1.

If costheta=(cosalpha-cosbeta)/(1-cosalpha.cosbeta) , prove that t a ntheta/2=+-tanalpha/2cotbeta/2 .

If cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-3/2 , prove that cosalpha+cosbeta+cosgamma=sinalpha+sinbeta+singamma=0

If costheta=(cosalpha cosbeta)/(1-sinalphasinbeta) , prove that one value of t a ntheta/2=(t a nalpha/2-t a nbeta/2)/(1-t a nalpha/2 t a nbeta/2)