What is the general solution for cos(4θ)=cos(3θ) ?

The general solution for cos(4θ)=cos(3θ) is θ=(4pin)/7 ,θ=(2pi)/7+(4pin)/7 ,θ=2pi+4pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(4θ)=cos(3θ)

cos (4 θ) = cos (3 θ)

θ = \frac{4 πn}{7}, θ = \frac{2 π}{7} + \frac{4 πn}{7}, θ = 2 π + 4 πn

Solution steps

cos (4 θ) = cos (3 θ)

Subtract

cos (3 θ)

from both sides

cos (4 θ) - cos (3 θ) = 0

Rewrite using trig identities

- 2 sin (\frac{7 θ}{2}) sin (\frac{θ}{2}) = 0

Solving each part separately

sin (\frac{7 θ}{2}) = 0 or sin (\frac{θ}{2}) = 0

sin (\frac{7 θ}{2}) = 0 : θ = \frac{4 πn}{7}, θ = \frac{2 π}{7} + \frac{4 πn}{7}

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

Combine all the solutions

θ = \frac{4 πn}{7}, θ = \frac{2 π}{7} + \frac{4 πn}{7}, θ = 4 πn, θ = 2 π + 4 πn

Merge Overlapping Intervals

θ = \frac{4 πn}{7}, θ = \frac{2 π}{7} + \frac{4 πn}{7}, θ = 2 π + 4 πn

\frac{- 2 3}{3} = sec (θ)

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

cot (x) = - 8

2 sin (x) cos (x) = cos^{2} (x)

- 1 + sin^{2} (a) + cos^{2} (a) = cos^{2} (a)

What is the general solution for cos(4θ)=cos(3θ) ?
The general solution for cos(4θ)=cos(3θ) is θ=(4pin)/7 ,θ=(2pi)/7+(4pin)/7 ,θ=2pi+4pin