What is the general solution for (cot(x)-1)(sin(x)-1)=0 ?

The general solution for (cot(x)-1)(sin(x)-1)=0 is x= pi/4+pin,x= pi/2+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(cot(x)-1)(sin(x)-1)=0

(cot (x) - 1) (sin (x) - 1) = 0

x = \frac{π}{4} + πn, x = \frac{π}{2} + 2 πn

Degrees

x = 4 5^{\circ} + 18 0^{\circ} n, x = 9 0^{\circ} + 36 0^{\circ} n

Solution steps

(cot (x) - 1) (sin (x) - 1) = 0

Solving each part separately

cot (x) - 1 = 0 or sin (x) - 1 = 0

cot (x) - 1 = 0 : x = \frac{π}{4} + πn

cot (x) - 1 = 0

Move

1

to the right side

cot (x) - 1 = 0

Add

1

to both sides

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

Simplify

cot (x) = 1

cot (x) = 1

General solutions for

cot (x) = 1

cot (x)

periodicity table with

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

sin (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

sin (x) - 1 = 0