What is the general solution for (sin(x)+cos(x))/(sin(x))=1 1/(tan(x)) ?

The general solution for (sin(x)+cos(x))/(sin(x))=1 1/(tan(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 >

(sin(x)+cos(x))/(sin(x))=1 1/(tan(x))

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

No Solution for x \in R

Solution steps

\frac{sin ( x ) + cos ( x )}{sin ( x )} = 1 \cdot \frac{1}{tan ( x )}

Subtract

1 \frac{1}{tan ( x )}

from both sides

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

Simplify

\frac{sin ( x ) + cos ( x )}{sin ( x )} - \frac{1}{tan ( x )} : \frac{tan ( x ) ( sin ( x ) + cos ( x ) ) - sin ( x )}{sin ( x ) tan ( x )}

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

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

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

Rewrite using trig identities

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

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

sin^{2} (x) = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

sin (x) = 0

General solutions for

sin (x) = 0

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 2 πn, x = π + 2 πn

Since the equation is undefined for:

2 πn, π + 2 πn

No Solution for x \in R

arctan (x) = \frac{- π}{2}

cot (θ) = - 3, sin (2 θ)

3 sin (2 x) - 1 cos (x) = 0

sin (4 x - 3) = cos (5 x - 6)

6 sin (2 x - 3 0^{\circ}) + 2 = 0

What is the general solution for (sin(x)+cos(x))/(sin(x))=1 1/(tan(x)) ?
The general solution for (sin(x)+cos(x))/(sin(x))=1 1/(tan(x)) is No Solution for x\in\mathbb{R}