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2cos^2(4x)=1

Solution

2 cos^{2} (4 x) = 1

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

Solution steps

2 cos^{2} (4 x) = 1

Solve by substitution

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

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

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

Combine all the solutions

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

sin (2 x) cos (x) + cos (2 x) sin (x) = \frac{1}{2}

csc^{2} (x) + 3 csc (x) + 2 = 0

2 sin (x) cos (x) + 2 cos (x) = 0

4.718 tan^{2} (θ) - 13.75 tan (θ) + 8.018 = 0

62 cos (θ) + 1 = 7