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

Prove the following: (frac(cosectheta+cottheta+1)(cottheta+cosectheta-1))=(frac(cottheta)(cosectheta-1))

Prove the following: (frac(1+cottheta+cosectheta)(1-cottheta-cosectheta))=(frac(cosectheta+cottheta-1)(cottheta-cosectheta+1))

Prove the following: (frac(cosectheta+cottheta-1)(cosectheta+cottheta+1))=(frac(1-sintheta)(costheta))

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

(tantheta + sintheta)/(tantheta - sintheta) =(sectheta + 1 )/ (sectheta -1)

Prove the following: tan2theta+sec2theta=(frac(1+tantheta)(1-tantheta))

Prove the following identities: (1+cottheta-cosectheta)(1+tantheta+sectheta)=2

Prove the following: (frac(1-cos2theta+sin2theta)(1+cos2theta+sin2theta))=tantheta

Prove the following: sqrt(frac(1-cos2theta)(1+cos2theta))=tantheta

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