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

The general solution for -cos(2x)+cos(x)=0 is x=(4pin)/3 ,x=(2pi)/3+(4pin)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = \frac{4 πn}{3}, x = \frac{2 π}{3} + \frac{4 πn}{3}

Solution steps

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

Rewrite using trig identities

2 sin (\frac{3 x}{2}) sin (\frac{x}{2}) = 0

Solving each part separately

sin (\frac{3 x}{2}) = 0 or sin (\frac{x}{2}) = 0

sin (\frac{3 x}{2}) = 0 : x = \frac{4 πn}{3}, x = \frac{2 π}{3} + \frac{4 πn}{3}

sin (\frac{x}{2}) = 0 : x = 4 πn, x = 2 π + 4 πn

Combine all the solutions

x = \frac{4 πn}{3}, x = \frac{2 π}{3} + \frac{4 πn}{3}, x = 4 πn, x = 2 π + 4 πn

Merge Overlapping Intervals

x = \frac{4 πn}{3}, x = \frac{2 π}{3} + \frac{4 πn}{3}

x, cos (x) + sin (y) = 1

2 sin (x) + 10 = 9

cos (x) = - \frac{3}{2}

sin^{2} (x) + 3 sin (x) + 1 = 0

8 sin (b) + 1 = sin (b) + 1

What is the general solution for -cos(2x)+cos(x)=0 ?
The general solution for -cos(2x)+cos(x)=0 is x=(4pin)/3 ,x=(2pi)/3+(4pin)/3