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

The general solution for sec(θ)= 1/(sin(θ)) is θ= pi/4+pin

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sec(θ)= 1/(sin(θ))

sec (θ) = \frac{1}{sin ( θ )}

θ = \frac{π}{4} + πn

Solution steps

sec (θ) = \frac{1}{sin ( θ )}

Subtract

\frac{1}{sin ( θ )}

from both sides

sec (θ) - \frac{1}{sin ( θ )} = 0

Simplify

sec (θ) - \frac{1}{sin ( θ )} : \frac{sec ( θ ) sin ( θ ) - 1}{sin ( θ )}

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

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

sec (θ) sin (θ) - 1 = 0

Rewrite using trig identities

- 1 + tan (θ) = 0

Move

1

to the right side

tan (θ) = 1

General solutions for

tan (θ) = 1

θ = \frac{π}{4} + πn

cos (x) = 1, 0 \leq x < 2 π

sin (t) = \frac{1}{3}

5 csc (x) - 3 = 2

2 cos^{2} (x) + 2 = 4

sin (z) = 3

What is the general solution for sec(θ)= 1/(sin(θ)) ?
The general solution for sec(θ)= 1/(sin(θ)) is θ= pi/4+pin