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

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

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sec(x)=tan(x)+cot(x)

sec (x) = tan (x) + cot (x)

No Solution for x \in R

Solution steps

sec (x) = tan (x) + cot (x)

Subtract

tan (x) + cot (x)

from both sides

sec (x) - tan (x) - cot (x) = 0

Express with sin, cos

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

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

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

Rewrite using trig identities

- 1 + sin (x) = 0

Move

1

to the right side

sin (x) = 1

General solutions for

sin (x) = 1

x = \frac{π}{2} + 2 πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn

No Solution for x \in R

cos (3 x) = - \frac{1}{2} 3

2 sin (2 x) + 3 = 0, 0 \leq x \leq 2 π

x, cos (x) = \frac{1}{3}

cos (θ) = - 0.02

cos^{2} (2 x) = 3 cos (2 x)

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