Prove that `cosectheta-cottheta=1/(cosectheta+cottheta)`

(cosectheta+cottheta)^2=

(cosectheta-cottheta)^2=

1+cottheta="cosec"theta

Prove that sintheta/(1-costheta)=cosectheta+cot theta

Prove that sqrt((cosec theta+cottheta)/(cosec theta-cottheta))=(sin theta)/(1-costheta)

Prove that- (1-costheta)/(1+costheta)=(cosectheta-cottheta)^2

Prove that- (1+costheta)/(1-costheta)= (cosectheta+cottheta)^2

Prove that- (1-costheta)/(1+costheta)=(1/(cosectheta+cottheta))^2

Prove that : (i) (1)/(sectheta-tantheta)+(1)/(sectheta+tantheta)=2sectheta " " (ii) ("cosec "theta+cottheta)/("cosec "theta-cottheta)=("cosec "theta+cottheta)^(2)

cosectheta=4/5 cottheta=?