What is the general solution for cos(4x)(cos(x)-1)=0 ?

The general solution for cos(4x)(cos(x)-1)=0 is x= pi/8+(pin)/2 ,x=(3pi)/8+(pin)/2 ,x=2pin

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cos(4x)(cos(x)-1)=0

cos (4 x) (cos (x) - 1) = 0

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{3 π}{8} + \frac{πn}{2}, x = 2 πn

Solution steps

cos (4 x) (cos (x) - 1) = 0

Solving each part separately

cos (4 x) = 0 or cos (x) - 1 = 0

cos (4 x) = 0 : x = \frac{π}{8} + \frac{πn}{2}, x = \frac{3 π}{8} + \frac{πn}{2}

cos (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = \frac{π}{8} + \frac{πn}{2}, x = \frac{3 π}{8} + \frac{πn}{2}, x = 2 πn

3 tan (\frac{x}{2}) + 3 = 0

4 cos (x) tan (x) = 5 tan (x)

4 cos^{2} (2 x) - 1 = 0

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

2 sin (x) - csc (x) = 1

What is the general solution for cos(4x)(cos(x)-1)=0 ?
The general solution for cos(4x)(cos(x)-1)=0 is x= pi/8+(pin)/2 ,x=(3pi)/8+(pin)/2 ,x=2pin