What is the general solution for cos(x)=cos(x-c) ?

The general solution for cos(x)=cos(x-c) is x=2pin+c/2 ,x=pi+2pin+c/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(x)=cos(x-c)

cos (x) = cos (x - c)

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

Solution steps

cos (x) = cos (x - c)

Subtract

cos (x - c)

from both sides

cos (x) - cos (x - c) = 0

Rewrite using trig identities

- 2 sin (\frac{c}{2}) sin (\frac{2 x - c}{2}) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

sin (\frac{2 x - c}{2}) = 0

General solutions for

sin (\frac{2 x - c}{2}) = 0

\frac{2 x - c}{2} = 0 + 2 πn, \frac{2 x - c}{2} = π + 2 πn

Solve

\frac{2 x - c}{2} = 0 + 2 πn : x = 2 πn + \frac{c}{2}

Solve

\frac{2 x - c}{2} = π + 2 πn : x = π + 2 πn + \frac{c}{2}

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

4 cos (120 t) = 0

\frac{3 3}{π} = sec (c)

2 \cdot sin^{2} (x) = sin (x)

tan (x) = \frac{1}{3}

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

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