What is the general solution for cos(2x+60)=sin(3x) ?

The general solution for cos(2x+60)=sin(3x) is x=(pi-120+4pin)/(10),x=pi-pi/2+60+2pin

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cos(2x+60)=sin(3x)

cos (2 x + 60) = sin (3 x)

x = \frac{π - 120 + 4 πn}{10}, x = π - \frac{π}{2} + 60 + 2 πn

Solution steps

cos (2 x + 60) = sin (3 x)

Rewrite using trig identities

cos (2 x + 60) = sin (\frac{π}{2} - (2 x + 60))

Apply trig inverse properties

3 x = \frac{π}{2} - (2 x + 60) + 2 πn, 3 x = π - (\frac{π}{2} - (2 x + 60)) + 2 πn

3 x = \frac{π}{2} - (2 x + 60) + 2 πn : x = \frac{π - 120 + 4 πn}{10}

3 x = π - (\frac{π}{2} - (2 x + 60)) + 2 πn : x = π - \frac{π}{2} + 60 + 2 πn

x = \frac{π - 120 + 4 πn}{10}, x = π - \frac{π}{2} + 60 + 2 πn

csc (θ) = - \frac{3}{2}

4 cos (θ) = 0

\frac{sin ( 16 0 ^{\circ} )}{5} = \frac{sin ( c )}{4}

sin (x) + 2 = 0

sin (θ) = - \frac{24}{25}

What is the general solution for cos(2x+60)=sin(3x) ?
The general solution for cos(2x+60)=sin(3x) is x=(pi-120+4pin)/(10),x=pi-pi/2+60+2pin