What is the general solution for cos^2(2x)=cos(4x) ?

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

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cos^2(2x)=cos(4x)

cos^{2} (2 x) = cos (4 x)

x = πn, x = \frac{π}{2} + πn

Solution steps

cos^{2} (2 x) = cos (4 x)

Subtract

cos (4 x)

from both sides

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

Rewrite using trig identities

sin^{2} (2 x) = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

sin (2 x) = 0

General solutions for

sin (2 x) = 0

2 x = 0 + 2 πn, 2 x = π + 2 πn

Solve

2 x = 0 + 2 πn : x = πn

Solve

2 x = π + 2 πn : x = \frac{π}{2} + πn

x = πn, x = \frac{π}{2} + πn

θ, tan (2 θ) = - 1

3 cos (z + 1.2) = 2

\frac{1}{2} = \frac{3}{2} \cdot cos (x)

cos (\frac{x}{2}) = - 12

4 sin (β) + 2 = 3 + 2 sin (β)

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