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

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

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

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

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

Solution steps

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

Subtract

3 csc (x) - 4

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

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

No Solution

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

Combine all the solutions

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

5 sin (θ) - 3 = 0

arctan (1 + x^{2}) = 0

θ, tan (θ) = - 1

2 sin (4 x) = - 4 sin (2 x)

cos (x) = (\frac{5}{3}), cot (2 x)

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