What is the general solution for sin(2x)sin(4x)=cos(2x)cos(4x) ?

The general solution for sin(2x)sin(4x)=cos(2x)cos(4x) is x= pi/(12)+(pin)/3 ,x= pi/4+(pin)/3

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sin(2x)sin(4x)=cos(2x)cos(4x)

sin (2 x) sin (4 x) = cos (2 x) cos (4 x)

x = \frac{π}{12} + \frac{πn}{3}, x = \frac{π}{4} + \frac{πn}{3}

Solution steps

sin (2 x) sin (4 x) = cos (2 x) cos (4 x)

Subtract

cos (2 x) cos (4 x)

from both sides

sin (2 x) sin (4 x) - cos (2 x) cos (4 x) = 0

Rewrite using trig identities

- cos (2 x + 4 x) = 0

Divide both sides by

- 1

cos (2 x + 4 x) = 0

General solutions for

cos (2 x + 4 x) = 0

2 x + 4 x = \frac{π}{2} + 2 πn, 2 x + 4 x = \frac{3 π}{2} + 2 πn

Solve

2 x + 4 x = \frac{π}{2} + 2 πn : x = \frac{π}{12} + \frac{πn}{3}

Solve

2 x + 4 x = \frac{3 π}{2} + 2 πn : x = \frac{π}{4} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}, x = \frac{π}{4} + \frac{πn}{3}

\frac{1}{sec ( θ )} = - \frac{7}{25}

3 tan^{3} (x) - 2 tan^{2} (x) - 32 tan (x) - 32 = 0

x, 2 sin (5 x) - 1 = 0

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

2 \cdot cos (2 x) + 1 = 0

What is the general solution for sin(2x)sin(4x)=cos(2x)cos(4x) ?
The general solution for sin(2x)sin(4x)=cos(2x)cos(4x) is x= pi/(12)+(pin)/3 ,x= pi/4+(pin)/3