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

The general solution for 4cos(x)=sqrt(2)+2cos(x) is x= pi/4+2pin,x=(7pi)/4+2pin

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4cos(x)=sqrt(2)+2cos(x)

4 cos (x) = 2 + 2 cos (x)

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Solution steps

4 cos (x) = 2 + 2 cos (x)

Solve by substitution

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

cos (x) = \frac{2}{2} : x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Combine all the solutions

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

4 cos (θ) = 43 sin (θ)

- 4 sin (θ) = 4 (sin (θ) - 1)

4 + 2 cos (θ) = 0

9.81 sin (θ) - 5.88 cos (θ) = 2.77

cos (θ) = π

What is the general solution for 4cos(x)=sqrt(2)+2cos(x) ?
The general solution for 4cos(x)=sqrt(2)+2cos(x) is x= pi/4+2pin,x=(7pi)/4+2pin