What is the general solution for cos(2x)+cos^2(x)=2 ?

The general solution for cos(2x)+cos^2(x)=2 is x=2pin,x=pi+2pin

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cos(2x)+cos^2(x)=2

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

2

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = 1, cos (x) = - 1

cos (x) = 1 : x = 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

tan^{2} (x) + 5 tan (x) - 7 = 0

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

cot^{2} (x) - 3 cot (x) = 0

x, y = sec (x)

tan (θ) = 2

What is the general solution for cos(2x)+cos^2(x)=2 ?
The general solution for cos(2x)+cos^2(x)=2 is x=2pin,x=pi+2pin