What is the general solution for 4csc(x)+sin(x)+5=0 ?

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

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4csc(x)+sin(x)+5=0

4 csc (x) + sin (x) + 5 = 0

x = \frac{3 π}{2} + 2 πn

Solution steps

4 csc (x) + sin (x) + 5 = 0

Rewrite using trig identities

5 + \frac{1}{csc ( x )} + 4 csc (x) = 0

Solve by substitution

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

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

No Solution

csc (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

tan (x) = 1087

- 3 sin (3 x) = 1

\frac{1}{cos ( x ) - cos ( x )} = sin (x) tan (x)

cos (θ) = \frac{3}{5} (270360)

2 sin (x) = tan (x) cos (x) - cos (x)

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