What is the general solution for 3csc(2x)-4sin(2x)=0 ?

The general solution for 3csc(2x)-4sin(2x)=0 is x= pi/6+pin,x= pi/3+pin,x=(2pi)/3+pin,x=(5pi)/6+pin

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3csc(2x)-4sin(2x)=0

3 csc (2 x) - 4 sin (2 x) = 0

x = \frac{π}{6} + πn, x = \frac{π}{3} + πn, x = \frac{2 π}{3} + πn, x = \frac{5 π}{6} + πn

Solution steps

3 csc (2 x) - 4 sin (2 x) = 0

Rewrite using trig identities

- \frac{4}{csc ( 2 x )} + 3 csc (2 x) = 0

Solve by substitution

csc (2 x) = \frac{2 3}{3}, csc (2 x) = - \frac{2 3}{3}

csc (2 x) = \frac{2 3}{3} : x = \frac{π}{6} + πn, x = \frac{π}{3} + πn

csc (2 x) = - \frac{2 3}{3} : x = \frac{2 π}{3} + πn, x = \frac{5 π}{6} + πn

Combine all the solutions

x = \frac{π}{6} + πn, x = \frac{π}{3} + πn, x = \frac{2 π}{3} + πn, x = \frac{5 π}{6} + πn

3 tan (B) - 4 = tan (B) - 2

sin (2 x) = 5 cos (2 x)

5 sec (2 x) + 2 = 0

2.1 sin (θ) = 1.33 sin (θ + 9 0^{\circ})

1 sin (4 5^{\circ}) = 1.33 sin (θ)

What is the general solution for 3csc(2x)-4sin(2x)=0 ?
The general solution for 3csc(2x)-4sin(2x)=0 is x= pi/6+pin,x= pi/3+pin,x=(2pi)/3+pin,x=(5pi)/6+pin