Prove that`sqrt(frac(cosecx-1)(cosecx+1))=(frac(1)(secx+tanx))`

intsqrt(cosecx-1)dx=

Prove the following: (frac(sec2A-1)(sec4A-1))=frac(tanA)(tan4A)

Prove that (frac(1+sintheta)(1+costheta)) + (frac(1-sintheta)(1-costheta)) = 2(cosec^2theta-cottheta)

Prove the following: (frac(cos(x-y))(cos(x+y)))=(frac(cotxcoty+1)(cotxcoty-1))

Prove that (cosecx-sinx)(secx-cosx)(tanx+cotx)=1

2tan^(-1)(cosx)=tan^(-1)(2cosecx)

Prove that (1tanx)^2+(1-cotx)^2=(secx-cosecx)^2

Prove that sqrt((1+sinx)/(1-sinx))=secx+tanx

Prove the following identities: (frac(1)(sectheta+tantheta))-(frac(1)(costheta))=(frac(1)(costheta))-(frac(1)(sectheta-tantheta))

Prove the following: if A+B=225^@ ,then prove that (frac(cotA)(1+cotA)).(frac(cotB)(1+cotB))=1/2