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

The general solution for 3-cos(2x)=4cos(2x) is x=(0.92729…)/2+pin,x=pi-(0.92729…)/2+pin

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

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

x = \frac{0.92729 \dots}{2} + πn, x = π - \frac{0.92729 \dots}{2} + πn

Solution steps

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

Solve by substitution

cos (2 x) = \frac{3}{5}

cos (2 x) = \frac{3}{5} : x = \frac{arccos ( \frac{3}{5} )}{2} + πn, x = π - \frac{arccos ( \frac{3}{5} )}{2} + πn

Combine all the solutions

x = \frac{arccos ( \frac{3}{5} )}{2} + πn, x = π - \frac{arccos ( \frac{3}{5} )}{2} + πn

Show solutions in decimal form

x = \frac{0.92729 \dots}{2} + πn, x = π - \frac{0.92729 \dots}{2} + πn

- 8 sin^{2} (x) + 22 sin (x) = 12

cos (θ) = \frac{1}{5}

sin^{2} (x) - 3 cos (x) + 3 = 0

cot^{2} (x) = cot^{2} (x) - 2 cot (x)

cos (x) = \frac{4}{10}

What is the general solution for 3-cos(2x)=4cos(2x) ?
The general solution for 3-cos(2x)=4cos(2x) is x=(0.92729…)/2+pin,x=pi-(0.92729…)/2+pin