What is the general solution for arctan(x+1)+arctan(x-1)=arctan(8/31) ?

The general solution for arctan(x+1)+arctan(x-1)=arctan(8/31) is x= 1/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

arctan(x+1)+arctan(x-1)=arctan(8/31)

arctan (x + 1) + arctan (x - 1) = arctan (\frac{8}{31})

x = \frac{1}{4}

Solution steps

arctan (x + 1) + arctan (x - 1) = arctan (\frac{8}{31})

Rewrite using trig identities

arctan (\frac{x + 1 + x - 1}{1 - ( x + 1 ) ( x - 1 )}) = arctan (\frac{8}{31})

Apply trig inverse properties

\frac{x + 1 + x - 1}{1 - ( x + 1 ) ( x - 1 )} = \frac{8}{31}

Solve

\frac{x + 1 + x - 1}{1 - ( x + 1 ) ( x - 1 )} = \frac{8}{31} : x = - 8, x = \frac{1}{4}

x = - 8, x = \frac{1}{4}

Verify solutions by plugging them into the original equation

x = \frac{1}{4}

4 cos (2 θ) + 19 = - 22 cos (θ) + 6

8 cos^{2} (x) + 16 cos (x) + 8 = 0

cos (x) = - 0.35

cos (x) = - 0.25

1 + sin^{2} (x) = cos^{2} (x)

What is the general solution for arctan(x+1)+arctan(x-1)=arctan(8/31) ?
The general solution for arctan(x+1)+arctan(x-1)=arctan(8/31) is x= 1/4