cos(x)-2sin(x)cos(x)=0,0<= x<= 2pi

Solution

cos (x) - 2 sin (x) cos (x) = 0, 0 \leq x \leq 2 π

x = \frac{π}{2}, x = \frac{3 π}{2}, x = \frac{π}{6}, x = \frac{5 π}{6}

Solution steps

cos (x) - 2 sin (x) cos (x) = 0, 0 \leq x \leq 2 π

Factor

cos (x) - 2 sin (x) cos (x) : - cos (x) (2 sin (x) - 1)

- cos (x) (2 sin (x) - 1) = 0

Solving each part separately

cos (x) = 0 or 2 sin (x) - 1 = 0

cos (x) = 0, 0 \leq x \leq 2 π : x = \frac{π}{2}, x = \frac{3 π}{2}

2 sin (x) - 1 = 0, 0 \leq x \leq 2 π : x = \frac{π}{6}, x = \frac{5 π}{6}

Combine all the solutions

x = \frac{π}{2}, x = \frac{3 π}{2}, x = \frac{π}{6}, x = \frac{5 π}{6}

sec^{2} (x) + 6 tan (x) = 8

tan (θ) = - \frac{3}{8}

i, arcsin (sin (x)) = x - 2 π

3 cos (2 θ) + 13 cos (θ) + 5 = 6 cos (θ)

tan (θ) = - \frac{3}{5}