What is the general solution for cos(x)-cos(3x)=0 ?

The general solution for cos(x)-cos(3x)=0 is x=pin,x= pi/2+pin

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cos(x)-cos(3x)=0

cos (x) - cos (3 x) = 0

x = πn, x = \frac{π}{2} + πn

Solution steps

cos (x) - cos (3 x) = 0

Rewrite using trig identities

2 sin (2 x) sin (x) = 0

Solving each part separately

sin (2 x) = 0 or sin (x) = 0

sin (2 x) = 0 : x = πn, x = \frac{π}{2} + πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

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

Merge Overlapping Intervals

x = πn, x = \frac{π}{2} + πn

5 cos (x) tan (x) + 3 tan (x) = 0

2 sec (θ) + 2 = 6

4 cos (x) tan (x) = 3 tan (x)

3 sin (x) = 1 + sin (x)

2 sin (x - \frac{π}{6}) + 1 = 0

What is the general solution for cos(x)-cos(3x)=0 ?
The general solution for cos(x)-cos(3x)=0 is x=pin,x= pi/2+pin