What is the general solution for 4cos(x)=3+8cos(x) ?

The general solution for 4cos(x)=3+8cos(x) is x=2.41885…+2pin,x=-2.41885…+2pin

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4cos(x)=3+8cos(x)

4 cos (x) = 3 + 8 cos (x)

x = 2.41885 \dots + 2 πn, x = - 2.41885 \dots + 2 πn

Solution steps

4 cos (x) = 3 + 8 cos (x)

Solve by substitution

cos (x) = - \frac{3}{4}

cos (x) = - \frac{3}{4} : x = arccos (- \frac{3}{4}) + 2 πn, x = - arccos (- \frac{3}{4}) + 2 πn

Combine all the solutions

x = arccos (- \frac{3}{4}) + 2 πn, x = - arccos (- \frac{3}{4}) + 2 πn

Show solutions in decimal form

x = 2.41885 \dots + 2 πn, x = - 2.41885 \dots + 2 πn

sin^{2} (θ) - 3 sin (θ) = 0

cos^{2} (x) = \frac{1}{5}

- 3 cos (2 θ) + 5 = 7 sin (θ) + 5

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

cos (θ) = - sin (θ)

What is the general solution for 4cos(x)=3+8cos(x) ?
The general solution for 4cos(x)=3+8cos(x) is x=2.41885…+2pin,x=-2.41885…+2pin