What is the general solution for 4+4cos(x)=-6cos(x) ?

The general solution for 4+4cos(x)=-6cos(x) is x=1.98231…+2pin,x=-1.98231…+2pin

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4+4cos(x)=-6cos(x)

4 + 4 cos (x) = - 6 cos (x)

x = 1.98231 \dots + 2 πn, x = - 1.98231 \dots + 2 πn

Solution steps

4 + 4 cos (x) = - 6 cos (x)

Solve by substitution

cos (x) = - \frac{2}{5}

cos (x) = - \frac{2}{5} : x = arccos (- \frac{2}{5}) + 2 πn, x = - arccos (- \frac{2}{5}) + 2 πn

Combine all the solutions

x = arccos (- \frac{2}{5}) + 2 πn, x = - arccos (- \frac{2}{5}) + 2 πn

Show solutions in decimal form

x = 1.98231 \dots + 2 πn, x = - 1.98231 \dots + 2 πn

2 cos (\frac{x}{2}) = 3, 0 \leq x \leq 2 π

sin (A) = \frac{4}{5}

3 tan^{2} (x) - 1 = 0, 0 \leq x \leq 2 π

sin (2 x) = 4 cos (x)

3 tan (2 x) - 1 = 0

What is the general solution for 4+4cos(x)=-6cos(x) ?
The general solution for 4+4cos(x)=-6cos(x) is x=1.98231…+2pin,x=-1.98231…+2pin