Question

if sinx + sin²x = 1, then cos⁸x + 2 cos⁶x + cos⁴ x​

Answer 1

Answer:

1

Step-by-step explanation:

sinx + sin²x = 1

sinx = 1 - sin²x

sinx = cos²x. 1...

since. cos²x + sin²x = 1

Now

cos⁸x + 2 cos⁶x + cos⁴ x

$= {sin}^{4} x + 2 {sin}^{3} x + {sin}^{2} x$

$= {sin}^{4} x + {sin}^{3} x + {sin}^{3} x + {sin}^{2} x$

$= {sin}^{2} x( {sin}^{2} x + sinx) + sinx( {sin}^{2} x + sinx)$

$= {sin}^{2} x + sinx$

$= 1$

Hope it helps

FOLLOW ME