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

The general solution for cos(2x)+1=2 is x=pin

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cos(2x)+1=2

cos (2 x) + 1 = 2

x = πn

Degrees

x = 0^{\circ} + 18 0^{\circ} n

Solution steps

cos (2 x) + 1 = 2

Move

1

to the right side

cos (2 x) + 1 = 2

Subtract

1

from both sides

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

Simplify

cos (2 x) = 1

cos (2 x) = 1

General solutions for

cos (2 x) = 1

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

2 x = 0 + 2 πn

2 x = 0 + 2 πn

Solve

2 x = 0 + 2 πn : x = πn

2 x = 0 + 2 πn

0 + 2 πn = 2 πn

2 x = 2 πn

Divide both sides by

2

2 x = 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{2 πn}{2}

Simplify

x = πn

x = πn

x = πn

csc (x) = - \frac{3}{5}

cos (x) = \frac{3}{5}, cos (2 π + x)

sin (4 5^{\circ}) = 1.57 \cdot sin (θ)

\frac{2}{3} = sec (x)

3 (cos (x) - 1) = - 1

What is the general solution for cos(2x)+1=2 ?
The general solution for cos(2x)+1=2 is x=pin