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

The general solution for cos^2(x)-sin^2(x)=2cos(x)-1 is x=2pin,x= pi/2+2pin,x=(3pi)/2+2pin

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

cos^{2} (x) - sin^{2} (x) = 2 cos (x) - 1

x = 2 πn, x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

cos^{2} (x) - sin^{2} (x) = 2 cos (x) - 1

Subtract

2 cos (x) - 1

from both sides

cos^{2} (x) - sin^{2} (x) - 2 cos (x) + 1 = 0

Rewrite using trig identities

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

Solve by substitution

cos (x) = 1, cos (x) = 0

cos (x) = 1 : x = 2 πn

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = 2 πn, x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

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

cos (θ) = \frac{6}{3 5}

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

4 sin (x) cos (x) - 2 cos (x) + 2 sin (x) - 1 = 0

tan (2 x) = 2 cot (2 x)

What is the general solution for cos^2(x)-sin^2(x)=2cos(x)-1 ?
The general solution for cos^2(x)-sin^2(x)=2cos(x)-1 is x=2pin,x= pi/2+2pin,x=(3pi)/2+2pin