What is the general solution for sec(θ)csc(θ)=1 ?

The general solution for sec(θ)csc(θ)=1 is No Solution for θ\in\mathbb{R}

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sec(θ)csc(θ)=1

sec (θ) csc (θ) = 1

No Solution for θ \in R

Solution steps

sec (θ) csc (θ) = 1

Subtract

1

from both sides

sec (θ) csc (θ) - 1 = 0

Express with sin, cos

\frac{1 - cos ( θ ) sin ( θ )}{cos ( 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

Divide both sides by

- 1

sin (2 θ) = 2

- 1 \leq sin (x) \leq 1

No Solution for θ \in R

cos (a + 27 0^{\circ}) = sin (a)

1 + sin (θ) = 2 - sin (θ)

- 4 cos^{2} (θ) + cos (θ) = 9 cos (θ) + 3

3 + 4 cot (x) = 5 csc (x)

(tan (x) - 1) (sec (x) + 1) = 0

What is the general solution for sec(θ)csc(θ)=1 ?
The general solution for sec(θ)csc(θ)=1 is No Solution for θ\in\mathbb{R}