What is the general solution for arctan(4-2x)=arctan(2x) ?

The general solution for arctan(4-2x)=arctan(2x) is x=1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

arctan(4-2x)=arctan(2x)

arctan (4 - 2 x) = arctan (2 x)

x = 1

Solution steps

arctan (4 - 2 x) = arctan (2 x)

Subtract

arctan (2 x)

from both sides

arctan (4 - 2 x) - arctan (2 x) = 0

Rewrite using trig identities

arctan (\frac{4 - 2 x - 2 x}{1 + ( 4 - 2 x ) \cdot 2 x}) = 0

Apply trig inverse properties

\frac{4 - 2 x - 2 x}{1 + ( 4 - 2 x ) \cdot 2 x} = 0

Solve

\frac{4 - 2 x - 2 x}{1 + ( 4 - 2 x ) \cdot 2 x} = 0 : x = 1

x = 1

Verify solutions by plugging them into the original equation

x = 1

tan (x) = tan (5 0^{\circ})

tan (θ) = 3, 0 < x < 2 π

cos (A) + 1 = 4 cos (A) + 1

3 cos (x) + 2 = 0

sin (θ) = 0.7 cos (9 0^{\circ} - θ)

What is the general solution for arctan(4-2x)=arctan(2x) ?
The general solution for arctan(4-2x)=arctan(2x) is x=1