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

The general solution for sin(3x)=cos(x) is x=(pi+4pin)/8 ,x=(pi+4pin)/4

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sin(3x)=cos(x)

sin (3 x) = cos (x)

x = \frac{π + 4 πn}{8}, x = \frac{π + 4 πn}{4}

Solution steps

sin (3 x) = cos (x)

Rewrite using trig identities

sin (3 x) = sin (\frac{π}{2} - x)

Apply trig inverse properties

3 x = \frac{π}{2} - x + 2 πn, 3 x = π - (\frac{π}{2} - x) + 2 πn

3 x = \frac{π}{2} - x + 2 πn : x = \frac{π + 4 πn}{8}

3 x = π - (\frac{π}{2} - x) + 2 πn : x = \frac{π + 4 πn}{4}

x = \frac{π + 4 πn}{8}, x = \frac{π + 4 πn}{4}

sin (5 x - 1 0^{\circ}) = \frac{2}{2}

tan (θ) = \frac{3}{6}

sinh (x) = \frac{9}{40}

12 sin (x) = 6

2 tan^{2} (x) - 5 tan (x) + 2 = 0

What is the general solution for sin(3x)=cos(x) ?
The general solution for sin(3x)=cos(x) is x=(pi+4pin)/8 ,x=(pi+4pin)/4