What is the general solution for (sin(2x))/(cos(x))=4+sin(2x)*tan(x) ?

The general solution for (sin(2x))/(cos(x))=4+sin(2x)*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(2x))/(cos(x))=4+sin(2x)*tan(x)

\frac{sin ( 2 x )}{cos ( x )} = 4 + sin (2 x) \cdot tan (x)

No Solution for x \in R

Solution steps

\frac{sin ( 2 x )}{cos ( x )} = 4 + sin (2 x) tan (x)

Subtract

4 + sin (2 x) tan (x)

from both sides

\frac{sin ( 2 x )}{cos ( x )} - 4 - sin (2 x) tan (x) = 0

Simplify

\frac{sin ( 2 x )}{cos ( x )} - 4 - sin (2 x) tan (x) : \frac{sin ( 2 x ) - 4 cos ( x ) - sin ( 2 x ) tan ( x ) cos ( x )}{cos ( x )}

\frac{sin ( 2 x ) - 4 cos ( x ) - sin ( 2 x ) tan ( x ) cos ( x )}{cos ( x )} = 0

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

sin (2 x) - 4 cos (x) - sin (2 x) tan (x) cos (x) = 0

Rewrite using trig identities

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

Factor

- 4 cos (x) + 2 cos (x) sin (x) - 2 cos^{2} (x) sin (x) tan (x) : 2 cos (x) (- 2 + sin (x) - cos (x) sin (x) tan (x))

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

Solving each part separately

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

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

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

No Solution

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn

No Solution for x \in R

sin (x) = 0.2174

x, arccot (x^{2}) y = arccot (x^{2})

\frac{50}{33} = \frac{sin ( x )}{sin ( 12 0 ^{\circ} - x )}

cot (x) csc (x) = cos (x)

2 tan (x) = 2

What is the general solution for (sin(2x))/(cos(x))=4+sin(2x)*tan(x) ?
The general solution for (sin(2x))/(cos(x))=4+sin(2x)*tan(x) is No Solution for x\in\mathbb{R}