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

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

Prove that (sinalpha)/(1+cosalpha)+(1+cosalpha)/(sin alpha)=2"cosec "alpha .

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

Prove that cosalpha/(sin3alpha)+(cos3alpha)/(sin9alpha)+(cos9alpha)/(sin27alpha)=1/2[cotalpha-cot27alpha]

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

Show that sqrt((1+cos alpha)/(1-cos alpha))=cosec alpha + cot alpha

1/(tan3alpha-tanalpha)-1/(cot3alpha-cotalpha)=cot2alpha

(sin alpha+csc alpha)^(2)+(cos alpha+sec alpha)^(2)-7=

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

The value of (cot^(2)alpha)((sec alpha-1)/(1+sin alpha))+sec^(2)alpha((sin alpha-1)/(1+sec alpha)) is