What is the general solution for 2csc(θ)=4cos(θ) ?

The general solution for 2csc(θ)=4cos(θ) is θ= pi/4+pin

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2csc(θ)=4cos(θ)

2 csc (θ) = 4 cos (θ)

θ = \frac{π}{4} + πn

Solution steps

2 csc (θ) = 4 cos (θ)

Subtract

4 cos (θ)

from both sides

2 csc (θ) - 4 cos (θ) = 0

Express with sin, cos

\frac{2 - 4 cos ( θ ) sin ( θ )}{sin ( θ )} = 0

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

2 - 4 cos (θ) sin (θ) = 0

Rewrite using trig identities

2 - 4 \cdot \frac{sin ( 2 θ )}{2} = 0

4 \cdot \frac{sin ( 2 θ )}{2} = 2 sin (2 θ)

2 - 2 sin (2 θ) = 0

Move

2

to the right side

- 2 sin (2 θ) = - 2

Divide both sides by

- 2

sin (2 θ) = 1

General solutions for

sin (2 θ) = 1

2 θ = \frac{π}{2} + 2 πn

Solve

2 θ = \frac{π}{2} + 2 πn : θ = \frac{π}{4} + πn

θ = \frac{π}{4} + πn

\frac{6}{5} arccos (\frac{y}{6}) = π

cos (x) = \frac{154}{212.85}

4 sin^{2} (x) - 2 = 0, 0 \leq x \leq 2 π

csc^{2} (θ) = 7 cot (θ) + 9

cos^{2} (x) + 6 cos (x) = - 3, y = 3

What is the general solution for 2csc(θ)=4cos(θ) ?
The general solution for 2csc(θ)=4cos(θ) is θ= pi/4+pin