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

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

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cos(4x)=cos(3x)

cos (4 x) = cos (3 x)

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

Solution steps

cos (4 x) = cos (3 x)

Subtract

cos (3 x)

from both sides

cos (4 x) - cos (3 x) = 0

Rewrite using trig identities

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

Solving each part separately

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

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

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

Combine all the solutions

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

Merge Overlapping Intervals

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

tan (x) + cot (x) = 2 sec (x)

12 sin^{2} (θ) = 9

2 cos (x) + 3 = 0, 0 \leq x \leq 2 π

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

tan (x) = 2.3

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