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

The general solution for (sec(x))/(cot(x)tan(x))=sin(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 >

(sec(x))/(cot(x)tan(x))=sin(x)

\frac{sec ( x )}{cot ( x ) tan ( x )} = sin (x)

No Solution for x \in R

Solution steps

\frac{sec ( x )}{cot ( x ) tan ( x )} = sin (x)

Subtract

sin (x)

from both sides

\frac{sec ( x )}{cot ( x ) tan ( x )} - sin (x) = 0

Simplify

\frac{sec ( x )}{cot ( x ) tan ( x )} - sin (x) : \frac{sec ( x ) - sin ( x ) cot ( x ) tan ( x )}{cot ( x ) tan ( x )}

\frac{sec ( x ) - sin ( x ) cot ( x ) tan ( x )}{cot ( x ) tan ( x )} = 0

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

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

Express with sin, cos

\frac{1 - cos ( x ) sin ( x )}{cos ( 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

Divide both sides by

- 1

sin (2 x) = 2

- 1 \leq sin (x) \leq 1

No Solution for x \in R

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

sin (θ) - 0.2 cos (θ) = 0.565

4 sin (θ) + 23 = 0

400 + 290 cos (x) + 290 sin (x) = 0

2 = 2 sin (2 θ)

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