What is the general solution for sin(3x)=cos(2x) ?

The general solution for sin(3x)=cos(2x) is x=(pi+4pin)/(10),x=pi-pi/2+2pin

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sin(3x)=cos(2x)

sin (3 x) = cos (2 x)

x = \frac{π + 4 πn}{10}, x = π - \frac{π}{2} + 2 πn

Solution steps

sin (3 x) = cos (2 x)

Rewrite using trig identities

sin (3 x) = sin (\frac{π}{2} - 2 x)

Apply trig inverse properties

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

3 x = \frac{π}{2} - 2 x + 2 πn : x = \frac{π + 4 πn}{10}

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

x = \frac{π + 4 πn}{10}, x = π - \frac{π}{2} + 2 πn

3 csc^{2} (θ) - 4 = 0

sin (x) = \frac{7}{9}

2 cos (t) = 0

10 sin (θ) + 8 = 11

4 cos (2 θ) = 0

What is the general solution for sin(3x)=cos(2x) ?
The general solution for sin(3x)=cos(2x) is x=(pi+4pin)/(10),x=pi-pi/2+2pin