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

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

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cos(3x)=sin(2x)

cos (3 x) = sin (2 x)

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

Solution steps

cos (3 x) = sin (2 x)

Rewrite using trig identities

cos (3 x) = sin (\frac{π}{2} - 3 x)

Apply trig inverse properties

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

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

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

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

sin (θ) = \frac{2}{3}, 9 0^{\circ} < θ < 18 0^{\circ}

4 sin^{2} (3 x) - 2 = 0

cos (\frac{π}{6} x) = 0

4 cos (θ) = - 4 sin (- θ)

tan (5 x) + tan (3 x) = 0

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