What is the general solution for cos(3x)-cos(7x)=0 ?

The general solution for cos(3x)-cos(7x)=0 is x=pin,x= pi/2+pin,x=(2pin)/5 ,x= pi/5+(2pin)/5

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cos(3x)-cos(7x)=0

cos (3 x) - cos (7 x) = 0

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

Solution steps

cos (3 x) - cos (7 x) = 0

Rewrite using trig identities

2 sin (2 x) sin (5 x) = 0

Solving each part separately

sin (2 x) = 0 or sin (5 x) = 0

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

sin (5 x) = 0 : x = \frac{2 πn}{5}, x = \frac{π}{5} + \frac{2 πn}{5}

Combine all the solutions

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

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

2 sin (x - 1) = 0

tan (x) = 0.42

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

0 = \frac{2}{3} cos (2 x) - \frac{2}{3} cos (x)

What is the general solution for cos(3x)-cos(7x)=0 ?
The general solution for cos(3x)-cos(7x)=0 is x=pin,x= pi/2+pin,x=(2pin)/5 ,x= pi/5+(2pin)/5