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 x= pi/4+pin

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

x = \frac{π}{4} + πn

Solution steps

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

Subtract

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

from both sides

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

Simplify

\frac{sin ( x ) + cos ( x )}{sin ( x )} - \frac{2}{tan ( x )} : \frac{tan ( x ) ( sin ( x ) + cos ( x ) ) - 2 sin ( x )}{sin ( x ) tan ( x )}

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

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

tan (x) (sin (x) + cos (x)) - 2 sin (x) = 0

Express with sin, cos

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

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

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

Factor

sin^{2} (x) - cos (x) sin (x) : sin (x) (sin (x) - cos (x))

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

Solving each part separately

sin (x) = 0 or sin (x) - cos (x) = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) - cos (x) = 0 : x = \frac{π}{4} + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + πn

Since the equation is undefined for:

2 πn, π + 2 πn

x = \frac{π}{4} + πn

3 tan (x + 4 5^{\circ}) = 3

0 = sin (π x)

sec (θ) csc (θ) = 1

cos (a + 27 0^{\circ}) = sin (a)

1 + sin (θ) = 2 - sin (θ)

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 x= pi/4+pin