If ` (2sinalpha)/(1+cosalpha +sinalpha)=y` , then prove that `(1-cosalpha+sinalpha )/(1+sinalpha)` is also equal to y.

If (2sinalpha)/({1+cos alpha+sin alpha})=y, then ({1-cos alpha+sin alpha})/(1+sin alpha)=

If A=[cosalpha+sinalpha,sqrt(2)sinalpha; -sqrt(2)sinalpha,cosalpha-sinalpha] , prove that A^n=[cosn\ alpha+sinn\ alpha, sqrt(2)sinn\ alpha; -sqrt(2)sinn\ alpha, cosn\ alpha-sinn\ alpha] for all n in Ndot

If cosalpha+cosbeta=0=sinalpha+sinbeta , then prove that cos2alpha +cos2beta=-2cos(alpha +beta) .

If 5tanalpha=4 , show that (5sinalpha-3cosalpha)/(5sinalpha+2cosalpha)=1/6

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

(sinalpha + cosalpha)(tanalpha + cotalpha) = secalpha + cosecalpha

If cosalpha+cosbeta=0=sinalpha+sinbeta , then prove that cos2alpha+cos2beta+2cos(alpha+beta)=0

If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) then show that sinalpha+cosalpha=sqrt(2)costheta .

If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) then show that sinalpha+cosalpha=sqrt(2)costheta .

If A= [[cosalpha,sinalpha],[-sinalpha,cosalpha]] then show that A^2=[[cos2alpha,sin2alpha],[-sin2alpha,cos2alpha]]