Prove that `(cotalpha+cosecalpha-1)/(cotalpha-cosecalpha+1)=(1+cosalpha)/sinalpha`

(cotalpha+"cosec"alpha-1)/(cotalpha-"cosec"alpha+1)=(1+cosalpha)/(sinalpha)

Prove that (sinalpha+cosalpha)(tanalpha+cotalpha)=secalpha+"cosec"alpha

Prove that cosalpha/(sin3alpha)+(cos3alpha)/(sin9alpha)+(cos9alpha)/(sin27alpha)=1/2[cotalpha-cot27alpha]

prove that, |{:(0,cosalpha,-sinalpha),(sinalpha,0,cosalpha),(cosalpha,sinalpha,0):}|^2=|{:(" "1,x,-x),(" "x,1," "x),(-x,x," "1):}| where x= sinalpha cosalpha

Prove that (1-cosalpha)/sinalpha=tan(alpha/2)

Prove that : (sinalpha+cosalpha)(tanalpha+cotalpha)=secalpha+"cosecα" .

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

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

Show that 1+cot^2alpha/(1+cosecalpha)=cosec alpha

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