`(1+cot alpha + cosec alpha)/(1-cot alpha + cosec alpha)=`

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

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

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

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 ]

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

(sin alpha)/(1+cos alpha)+(1+cos alpha)/(sin alpha)=2cosec alpha

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

If (sin alpha + "cosec" alpha )^(2) + ( cos alpha + sec alpha )^(2)=k+ tan^(2) alpha + cot^(2) alpha then k=

Prove that: (tan^(3)alpha)/(1+tan^(2)alpha)+(cot^(3)alpha)/(1+cot^(2)alpha)=sec alpha cosec alpha-2sin alpha cos alpha