What is the general solution for cos(5θ)=cos(3θ) ?

The general solution for cos(5θ)=cos(3θ) is θ=(pin)/2 ,θ= pi/4+(pin)/2 ,θ=2pin,θ=pi+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(5θ)=cos(3θ)

cos (5 θ) = cos (3 θ)

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

Solution steps

cos (5 θ) = cos (3 θ)

Subtract

cos (3 θ)

from both sides

cos (5 θ) - cos (3 θ) = 0

Rewrite using trig identities

- 2 sin (4 θ) sin (θ) = 0

Solving each part separately

sin (4 θ) = 0 or sin (θ) = 0

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

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

Combine all the solutions

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

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

8 \cdot sin^{2} (2 x) - 2 \cdot sin (2 x) - 1 = 0

4 - 2 cos (2 x) = 0

x, 2 cos^{2} (x) + sin (x) = 1

2 cos^{2} (x) + 6 cos (x) = - 1

What is the general solution for cos(5θ)=cos(3θ) ?
The general solution for cos(5θ)=cos(3θ) is θ=(pin)/2 ,θ= pi/4+(pin)/2 ,θ=2pin,θ=pi+2pin