What is the general solution for 5cos(2x)+1=3cos(2x) ?

The general solution for 5cos(2x)+1=3cos(2x) is x= pi/3+pin,x=(2pi)/3+pin

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5cos(2x)+1=3cos(2x)

5 cos (2 x) + 1 = 3 cos (2 x)

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

Solution steps

5 cos (2 x) + 1 = 3 cos (2 x)

Solve by substitution

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

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

Combine all the solutions

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

2 sin (4 x) + 6 = 5

7 sin (x) tan (x) = - 8 tan (x)

sin^{2} (x) + 2 sin (x) - 3 = 0

sin^{2} (x) - tan (x) cos^{2} (x) = 0

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

What is the general solution for 5cos(2x)+1=3cos(2x) ?
The general solution for 5cos(2x)+1=3cos(2x) is x= pi/3+pin,x=(2pi)/3+pin