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

The general solution for cos(θ)=csc(θ) is No Solution for θ\in\mathbb{R}

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cos(θ)=csc(θ)

cos (θ) = csc (θ)

No Solution for θ \in R

Solution steps

cos (θ) = csc (θ)

Subtract

csc (θ)

from both sides

cos (θ) - csc (θ) = 0

Express with sin, cos

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

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

- 1 + cos (θ) sin (θ) = 0

Rewrite using trig identities

- 1 + \frac{sin ( 2 θ )}{2} = 0

Move

1

to the right side

\frac{sin ( 2 θ )}{2} = 1

Multiply both sides by

2

sin (2 θ) = 2

- 1 \leq sin (x) \leq 1

No Solution for θ \in R

0 = sin^{2} (x) - sin (x)

cos (2 x) + cos (x) = 2

sec^{2} (θ) + 2 tan (θ) = 0

4 sin^{2} (\frac{x}{2}) + 8 cos (\frac{x}{2}) - 7 = 0

sin (x) + cos (x) = 1, - 36 0^{\circ} \leq x \leq 36 0^{\circ}

What is the general solution for cos(θ)=csc(θ) ?
The general solution for cos(θ)=csc(θ) is No Solution for θ\in\mathbb{R}