What is the general solution for 4csc(x)+2sin(x)=9 ?

The general solution for 4csc(x)+2sin(x)=9 is x= pi/6+2pin,x=(5pi)/6+2pin

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4csc(x)+2sin(x)=9

4 csc (x) + 2 sin (x) = 9

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

Solution steps

4 csc (x) + 2 sin (x) = 9

Subtract

9

from both sides

4 csc (x) + 2 sin (x) - 9 = 0

Rewrite using trig identities

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

Solve by substitution

csc (x) = 2, csc (x) = \frac{1}{4}

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

csc (x) = \frac{1}{4} :

No Solution

Combine all the solutions

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

x, h = 1 + sin (π x)

1 - cos (θ) = sin (\frac{θ}{2})

cos (\frac{θ}{3} + 2 4^{\circ}) = sin (θ)

- 4 + 4 sin (x) = - 2

sin (x + π) + sin (x - π) = 0

What is the general solution for 4csc(x)+2sin(x)=9 ?
The general solution for 4csc(x)+2sin(x)=9 is x= pi/6+2pin,x=(5pi)/6+2pin