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

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

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sin(x)=cos(3x)

sin (x) = cos (3 x)

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

Solution steps

sin (x) = cos (3 x)

Rewrite using trig identities

sin (x) = sin (\frac{π}{2} - 3 x)

Apply trig inverse properties

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

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

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

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

x, y = 5 sin (\frac{x}{4})

3 sin (\frac{π}{3} x) = 2

cos^{2} (x) = \frac{1}{3}

4 cos (θ) = 1 + 2 cos (θ)

tan (θ) = \frac{3}{3}

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