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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cot(x)tan(x)=(sec(x))(csc(x))

cot (x) tan (x) = (sec (x)) (csc (x))

No Solution for x \in R

Solution steps

cot (x) tan (x) = (sec (x)) (csc (x))

Subtract

sec (x) csc (x)

from both sides

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

Express with sin, cos

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

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

- 1 + cos (x) sin (x) = 0

Rewrite using trig identities

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

Move

1

to the right side

\frac{sin ( 2 x )}{2} = 1

Multiply both sides by

2

sin (2 x) = 2

- 1 \leq sin (x) \leq 1

No Solution for x \in R

sin (2 x) = 5 cos^{2} (x)

2 sin^{2} (x) - 3 sin (x) + 1 = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

sin^{2} (θ) + cos (θ) = 2

cot (2 x) - 1 = 0

tan (2 θ) - tan (θ) = 0, 0 < θ < 2 π

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