What is the general solution for cos(x)= 1/(cot(x)) ?

The general solution for cos(x)= 1/(cot(x)) is x=0.66623…+2pin,x=pi-0.66623…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(x)= 1/(cot(x))

cos (x) = \frac{1}{cot ( x )}

x = 0.66623 \dots + 2 πn, x = π - 0.66623 \dots + 2 πn

Solution steps

cos (x) = \frac{1}{cot ( x )}

Subtract

\frac{1}{cot ( x )}

from both sides

cos (x) - \frac{1}{cot ( x )} = 0

Simplify

cos (x) - \frac{1}{cot ( x )} : \frac{cos ( x ) cot ( x ) - 1}{cot ( x )}

\frac{cos ( x ) cot ( x ) - 1}{cot ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Rewrite using trig identities

- 1 + \frac{1 - sin ^{2} ( x )}{sin ( x )} = 0

Solve by substitution

sin (x) = - \frac{1 + 5}{2}, sin (x) = \frac{5 - 1}{2}

sin (x) = - \frac{1 + 5}{2} :

No Solution

sin (x) = \frac{5 - 1}{2} : x = arcsin (\frac{5 - 1}{2}) + 2 πn, x = π - arcsin (\frac{5 - 1}{2}) + 2 πn

Combine all the solutions

x = arcsin (\frac{5 - 1}{2}) + 2 πn, x = π - arcsin (\frac{5 - 1}{2}) + 2 πn

Show solutions in decimal form

x = 0.66623 \dots + 2 πn, x = π - 0.66623 \dots + 2 πn

(sin (x) - 1) \cdot (sin (x) - 3) = 0

2 - 3 cos (θ) = 0

2 sin (x) cos (x) = 0, 0 \leq x \leq 2 π

tan (θ) = - \frac{3}{4}, sec (θ)

\frac{12}{sin ( 12 0 ^{\circ} )} = \frac{5}{sin ( x )}

What is the general solution for cos(x)= 1/(cot(x)) ?
The general solution for cos(x)= 1/(cot(x)) is x=0.66623…+2pin,x=pi-0.66623…+2pin