Cosa + Sina =2 then what is value of cos^na + sin^na=?

sin and csc are reciprocal functions meaning cscA = 1/sinA

therefore sin8Acsc8A = sin8A / sin8A = 1

this answer was determined regardless of the fact that the problem says sinA + cscA = 2

however you can determine from this first equation that sinA = 1 and therefore cscA = 1 as well

intuitively you can say to yourself that the maximum value of sin is 1, so if sinA + 1/sinA = 2, this is only possible when sinA is 1