10sin^2(4x)=5

Solution

10 sin^{2} (4 x) = 5

x = \frac{π}{16} + \frac{πn}{2}, x = \frac{3 π}{16} + \frac{πn}{2}, x = \frac{5 π}{16} + \frac{πn}{2}, x = \frac{7 π}{16} + \frac{πn}{2}

Solution steps

10 sin^{2} (4 x) = 5

Solve by substitution

sin (4 x) = \frac{1}{2}, sin (4 x) = - \frac{1}{2}

sin (4 x) = \frac{1}{2} : x = \frac{π}{16} + \frac{πn}{2}, x = \frac{3 π}{16} + \frac{πn}{2}

sin (4 x) = - \frac{1}{2} : x = \frac{5 π}{16} + \frac{πn}{2}, x = \frac{7 π}{16} + \frac{πn}{2}

Combine all the solutions

x = \frac{π}{16} + \frac{πn}{2}, x = \frac{3 π}{16} + \frac{πn}{2}, x = \frac{5 π}{16} + \frac{πn}{2}, x = \frac{7 π}{16} + \frac{πn}{2}

cosh (x) = 2

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

- 2 cos (3 θ) = 1

sec^{2} (x) + 0.5 tan (x) - 1 = 0

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