Question

Find all solutions of the equation in the interval [0, 2π).

Answer 1

Answer:

x=0

Step-by-step explanation:

$4 \cos(x) = - \sin {}^{2} (x) + 1$

$4 \cos(x) = 1 - \sin {}^{2} (x)$

$4 \cos(x) = \cos {}^{2} (x)$

$4 \cos(x) - \cos {}^{2} (x) = 0$

$\cos(x) (4 - \cos(x) ) = 0$

$\cos(x) = 0$

$x = 0$

$4 - \cos(x) = 0$

$\cos(x) = 4$

There is no solution here because cosine is undefined it the range is not between -1 and 1 so the only answer is 0.