If `tanalpha=(asinbeta)/(1-acosbeta)`and `tanbeta=(bsinalpha)/(1-bcosalpha)`,prove that `bsinalpha=asinbeta`

Prove that 0!=1

If tanbeta=(nsinalphacosalpha)/(1-nsin^2alpha) ,show that tan(alpha-beta)=(1-n)tanalpha

If sinalphasinbeta-cosalphacosbeta+1=0 prove that 1+cotalphatanbeta=0

If tan alpha=m/(m+1) and tan beta=1/(2m+1) ,prove that alpha+beta=pi/4 .

If alpha and beta be two acute angles and cos2alpha=(3cos2beta-1)/(3-cos2beta) ,show that tan alpha=sqrt2tanbeta

If sin(theta+alpha)=nsin(theta-alpha) and n!=-1 ,prove that cottheta=(n-1)/(n+1)cotalpha

Prove that sintheta/(1+costheta) + (1+costheta)/sintheta = 2cosectheta

If sintheta - costheta = 1 , then prove that sintheta + costheta =+-1

Prove that (1-sintheta)/(1+sintheta)=(sectheta-tantheta)^2 .

Prove the following (1 + sectheta) /(sectheta )=(sin^2theta) /(1-costheta)