What is the general solution for sec(θ)=tan(θ)+cot(θ) ?

The general solution for sec(θ)=tan(θ)+cot(θ) is No Solution for θ\in\mathbb{R}

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sec(θ)=tan(θ)+cot(θ)

sec (θ) = tan (θ) + cot (θ)

No Solution for θ \in R

Solution steps

sec (θ) = tan (θ) + cot (θ)

Subtract

tan (θ) + cot (θ)

from both sides

sec (θ) - tan (θ) - cot (θ) = 0

Express with sin, cos

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

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

- cos^{2} (θ) + (1 - sin (θ)) sin (θ) = 0

Rewrite using trig identities

- 1 + sin (θ) = 0

Move

1

to the right side

sin (θ) = 1

General solutions for

sin (θ) = 1

θ = \frac{π}{2} + 2 πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn

No Solution for θ \in R

sec^{2} (x) = \frac{4}{3}, 0 \leq x \leq 2 π

3 tan (3 θ) - 1 = 0

2 tan (x) = sec (x)

cos (x) = 2 π

sin (6 x) + sin (2 x) = 0

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