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

int(1)/(sqrt(sin^(3)xsin(x+alpha)))dx,alpha!=npi,nin Z is equal to a) -2" cosec "alpha(cosalpha-tanxsinalpha)^(1//2)+C b) -2(cosalpha+cotxsinalpha)^(1//2)+C c) -2" cosec "alpha(cosalpha+cotxsin alpha)^(1//2)+C d) -2" cosec "alpha(sinalpha+cotxcosalpha)^(1//2)+C

(sinalpha + cosalpha)(tanalpha + cotalpha) = secalpha + cosecalpha

(sinalpha + cosalpha)(tanalpha + cotalpha) = secalpha + cosecalpha

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

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

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

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

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

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