What is the general solution for -cos(2x)=2cos(2x)-1 ?

The general solution for -cos(2x)=2cos(2x)-1 is x=(1.23095…)/2+pin,x=pi-(1.23095…)/2+pin

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-cos(2x)=2cos(2x)-1

- cos (2 x) = 2 cos (2 x) - 1

x = \frac{1.23095 \dots}{2} + πn, x = π - \frac{1.23095 \dots}{2} + πn

Solution steps

- cos (2 x) = 2 cos (2 x) - 1

Solve by substitution

cos (2 x) = \frac{1}{3}

cos (2 x) = \frac{1}{3} : x = \frac{arccos ( \frac{1}{3} )}{2} + πn, x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

Combine all the solutions

x = \frac{arccos ( \frac{1}{3} )}{2} + πn, x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

Show solutions in decimal form

x = \frac{1.23095 \dots}{2} + πn, x = π - \frac{1.23095 \dots}{2} + πn

sin (x) = 23

sin (A) = \frac{3}{2}

sin (θ) = \frac{3}{5}, tan (θ)

sin^{22} (x) = 0.5

arctan (z) = \frac{π}{2}

What is the general solution for -cos(2x)=2cos(2x)-1 ?
The general solution for -cos(2x)=2cos(2x)-1 is x=(1.23095…)/2+pin,x=pi-(1.23095…)/2+pin