What is the general solution for cos^3(x)=cos(2x+x) ?

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

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cos^3(x)=cos(2x+x)

cos^{3} (x) = cos (2 x + x)

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

Solution steps

cos^{3} (x) = cos (2 x + x)

Subtract

cos (2 x + x)

from both sides

cos^{3} (x) - cos (3 x) = 0

Rewrite using trig identities

3 cos (x) - 3 cos^{3} (x) = 0

Solve by substitution

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

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

cos (x) = - 1 : x = π + 2 πn

cos (x) = 1 : x = 2 πn

Combine all the solutions

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

x, (d^{2} - 3 d + 2) y = sin (e^{x})

cos (6 x) + cos (2 x) = 0

2 sin^{2} (4 5^{\circ} - a) = 1 - sin^{2} (a)

(2 cos (a) + 1) (2 cos (a) - 1) = 2 cos^{2} (a) + 1

tan^{2} (x) cot (x) = 1

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