What is the general solution for cos(2x)(cos(2x)-3)=0 ?

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

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cos(2x)(cos(2x)-3)=0

cos (2 x) (cos (2 x) - 3) = 0

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

Solution steps

cos (2 x) (cos (2 x) - 3) = 0

Solving each part separately

cos (2 x) = 0 or cos (2 x) - 3 = 0

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

cos (2 x) - 3 = 0 :

No Solution

Combine all the solutions

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

csc^{2} (x) = 9

csc^{2} (x) = 3

cos (x) sin (x) + 3 sin (x) = 0

3 - 3 cos^{2} (θ) = 1 + sin^{2} (θ)

33 cot (θ) + 6 = 9

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