What is the general solution for 1+cos(2t)=cos^2(t) ?

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

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1+cos(2t)=cos^2(t)

1 + cos (2 t) = cos^{2} (t)

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

Solution steps

1 + cos (2 t) = cos^{2} (t)

Subtract

cos^{2} (t)

from both sides

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

Rewrite using trig identities

1 - sin^{2} (t) = 0

Solve by substitution

sin (t) = 1, sin (t) = - 1

sin (t) = 1 : t = \frac{π}{2} + 2 πn

sin (t) = - 1 : t = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

2 sin (2 x + \frac{3 π}{2}) + 1 = 0

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

2 cos^{2} (θ) - 2 sin^{2} (θ) = 2

cot (θ) + 3 csc (θ) = 5

2 cos^{2} (θ) - 2 sin^{2} (θ) = 3

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