What is the general solution for (cos(x)-1)(cos(x)-2)=0 ?

The general solution for (cos(x)-1)(cos(x)-2)=0 is x=2pin

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

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

x = 2 πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n

Solution steps

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

Solving each part separately

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

cos (x) - 1 = 0 : x = 2 πn

cos (x) - 1 = 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 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

cos (x) - 2 = 0 :

No Solution

cos (x) - 2 = 0

Move

2

to the right side

cos (x) - 2 = 0

Add

2

to both sides

cos (x) - 2 + 2 = 0 + 2

Simplify

cos (x) = 2

cos (x) = 2

- 1 \leq cos (x) \leq 1

No Solution

Combine all the solutions

x = 2 πn

tan (θ) = \frac{4}{- 3}

tan (3 x + 2 6^{\circ}) = cot (5 x)

sin (x) = \frac{3}{5}, \frac{π}{2} \leq x \leq π

2 sin^{2} (θ) + cos (θ) = 2

x, - 31 y = sin (x)

What is the general solution for (cos(x)-1)(cos(x)-2)=0 ?
The general solution for (cos(x)-1)(cos(x)-2)=0 is x=2pin