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

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

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

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

x = \frac{3 π}{2} + 2 πn

Solution steps

sin (x) + 4 csc (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

sin (x) = \frac{5}{9}

sin (x) = \frac{5}{3}

tan (3 x) = \frac{1}{3}

7 cot (x) - 3 = 4 cot (x)

cos (θ) + 2 cos^{2} (θ) = 1

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