Question

If sin²a + sina = 1 then prove that
Cos¹²a + 3Cos^10 a+ 3cos^8 a + cos^6 a-1 = 0.

I am using a in the place of theta.

Answer 1

cos12 a +3cos 10a+3cos 8a+cos 6a-1

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 !!