(cot theta+cos ee alpha-1)/(cot Q-cosec Q+1)=(1+cos alpha)/(sin alpha)

Prove that (cot alpha+cos ec alpha-1)/(cot alpha-cos ec alpha+1)=(1+cos alpha)/(sin alpha)

(cot theta+csc theta-1)/(cot theta-csc theta+1)=(1+cos theta)/(sin theta)

Prove that (cot theta + "cosec" theta -1 )/(cot theta - "cosec" theta +1)=(1+ cos theta)/(sin theta).

Prove that (cot theta + "cosec" theta -1 )/(cot theta - "cosec" theta +1)=(1+ cos theta)/(sin theta).

If x=a ( " cosec " alpha + cot alpha) and y=(b(1- cos alpha))/(sin alpha ) , then

1/(cos alpha + cos 3 alpha)+ 1/(cos alpha + cos 5 alpha)+ 1/(cos alpha + cos 7 alpha) +....+ 1/(cos alpha +cos(2n+1) alpha) = 1/2 "cosec" alpha[tan (n+1) alpha - tan alpha ]

Prove that (1)/("cosec"alpha-cot alpha)-(1)/(sin alpha)=(1)/(sin alpha)-(1)/("cosec"alpha+cotalpha) .

(1+cot alpha+cos ec alpha)/(1-cot alpha+cos ec alpha)=

(1+cot alpha+cos ec alpha)/(1-cot alpha+cos ec alpha)=