What is the general solution for cos(2x)+4cos(x)=-3 ?

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

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cos(2x)+4cos(x)=-3

cos (2 x) + 4 cos (x) = - 3

x = π + 2 πn

Solution steps

cos (2 x) + 4 cos (x) = - 3

Subtract

- 3

from both sides

cos (2 x) + 4 cos (x) + 3 = 0

Rewrite using trig identities

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

Solve by substitution

cos (x) = - 1

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = π + 2 πn

1 = 2 cos (2 x)

cos (\frac{π}{6}) = sin (x)

cos (θ) = - \frac{9}{10}

arctan (x) = \frac{1}{2}

tan (2 θ) = 2

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