Question

8 sin2 x + cos x - 5 = 0

Answer 1

$8 {sin}^{2} x + cos \: x - 5 = 0$

$recall \: that \: {sin}^{2} x + {cos}^{2} x = 1$

$then \: {sin}^{2} x = 1 - {cos}^{2} x$

then substitute,

$8( 1 - {cos}^{2} x) + cos \: x - 5 = 0$

After Further Simplication,

$8 {cos}^{2} x - cos \: x - 3 = 0$

$let \: y = \cos(x)$

$8 {y}^{2} - y - 3 = 0$

use quadratic formulae

$y = 0.375 \: or \: - 0.25$

therefore

$\cos(x) = 0.375 \: or \: - 0.25$

$x = 70degrees \: or \: 104.5degrees$