What is the general solution for 2csc(θ)=sqrt(2)cot(θ)+3csc(θ) ?

The general solution for 2csc(θ)=sqrt(2)cot(θ)+3csc(θ) is θ=(3pi)/4+2pin,θ=(5pi)/4+2pin

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2csc(θ)=sqrt(2)cot(θ)+3csc(θ)

2 csc (θ) = 2 cot (θ) + 3 csc (θ)

θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

Solution steps

2 csc (θ) = 2 cot (θ) + 3 csc (θ)

Subtract

2 cot (θ) + 3 csc (θ)

from both sides

- csc (θ) - 2 cot (θ) = 0

Express with sin, cos

\frac{- 1 - cos ( θ ) 2}{sin ( θ )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- 1 - cos (θ) 2 = 0

Move

1

to the right side

- cos (θ) 2 = 1

Divide both sides by

- 2

cos (θ) = - \frac{2}{2}

General solutions for

cos (θ) = - \frac{2}{2}

θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

sin (\frac{1}{2} x) = - 1

9 cos^{2} (x) tan (x) = 4 tan (x)

3 tan (x) - 3 = 0, 0 \leq x \leq 2 π

\frac{sin ( 57.2 2 ^{\circ} )}{31.5} = \frac{sin ( Q )}{24.4}

cosh (x) = 10

What is the general solution for 2csc(θ)=sqrt(2)cot(θ)+3csc(θ) ?
The general solution for 2csc(θ)=sqrt(2)cot(θ)+3csc(θ) is θ=(3pi)/4+2pin,θ=(5pi)/4+2pin