If Sin a+ sin²a=1 then,find the value of cos¹² a +3cos ¹⁰a+3cos ⁸a+cos ⁶a-1

Dear student,

can be written as [cos^2 a + cos^4 a]^3 - 1

from given equation sin^2 a  = 1 - sin a => cos^2 a = sin a

=> [ sina a + sin^2 a ]^3 - 1 

=> 1^3 - 1

=> 0

hope it explains !!