Question

| sinx cosx 1 |
| (sinx)^2 (cosx)^2 1 |
| (sinx)^3 (cosx)^3 1 |

Evaluate and factorise the determinant of the matrix.

Answer 1

for starters
s *c^2 + c*s^3 + c^3*s^2 - c^2s^3 - sc^3 -s^2 c
s c [ c + s^2 + c^2 s - c s^2 - c^2 - s ]

Answer 2

It's never going to get very simple, but one factorization is
1/4 (c-s)((c+s)^2 - 1)(c+s-1)^2