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

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

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cos(2a)=1

cos (2 a) = 1

a = πn

Degrees

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

Solution steps

cos (2 a) = 1

General solutions for

cos (2 a) = 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 a = 0 + 2 πn

2 a = 0 + 2 πn

Solve

2 a = 0 + 2 πn : a = πn

2 a = 0 + 2 πn

0 + 2 πn = 2 πn

2 a = 2 πn

Divide both sides by

2

2 a = 2 πn

Divide both sides by

2

\frac{2 a}{2} = \frac{2 πn}{2}

Simplify

a = πn

a = πn

a = πn

cos (\frac{2}{3} x) = 0

sin (2 x) cos (2 x) = 2

\frac{cos ( t )}{3 cos ( 3 t )} = 0

3 tan (3 x) = 1

x, cos (x) + 3 = - cos (x)

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