What is the general solution for cos(x)(cos(x)-1)=0,n=0 ?

The general solution for cos(x)(cos(x)-1)=0,n=0 is x=0

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

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

x = 0

Degrees

x = 0^{\circ}

Solution steps

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

Solving each part separately

cos (x) = 0 or cos (x) - 1 = 0

cos (x) = 0, n = 0 :

No Solution

cos (x) = 0, n = 0

General solutions for

cos (x) = 0

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}

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

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

Solutions for the range

n = 0

No Solution

cos (x) - 1 = 0, n = 0 : x = 0

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

Move

1

to the right side

cos (x) - 1 = 0

Add

1

to both sides

cos (x) - 1 + 1 = 0 + 1

Simplify

cos (x) = 1

cos (x) = 1

General solutions for

cos (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}

x = 0 + 2 πn

x = 0 + 2 πn

Solve

x = 0 + 2 πk : x = 2 πk

x = 0 + 2 πk

0 + 2 πk = 2 πk

x = 2 πk

x = 2 πk

Solutions for the range

n = 0

x = 0

Combine all the solutions

x = 0

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

tan (2 x) = - 1.238

tan (θ) = π

csc^{2} (x) + 2 cot^{2} (x) = 1

3 csc (2 x) + 2 = 0

What is the general solution for cos(x)(cos(x)-1)=0,n=0 ?
The general solution for cos(x)(cos(x)-1)=0,n=0 is x=0