What is tan(arctan(x)+pi/4) ?

The solution to tan(arctan(x)+pi/4) is (x+1)/(1-x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify tan(arctan(x)+pi/4)

simplify

tan (arctan (x) + \frac{π}{4})

\frac{x + 1}{1 - x}

Solution steps

tan (arctan (x) + \frac{π}{4})

Rewrite using trig identities

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

Use the following identity:

cos (arctan (x)) = \frac{1 + x ^{2}}{1 + x ^{2}}

= \frac{sin ( arctan ( x ) ) + ( \frac{1 + x ^{2}}{1 + x ^{2}} )}{( \frac{1 + x ^{2}}{1 + x ^{2}} ) - sin ( arctan ( x ) )}

Use the following identity:

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

= \frac{( \frac{x 1 + x ^{2}}{1 + x ^{2}} ) + ( \frac{1 + x ^{2}}{1 + x ^{2}} )}{( \frac{1 + x ^{2}}{1 + x ^{2}} ) - ( \frac{x 1 + x ^{2}}{1 + x ^{2}} )}

Simplify

= \frac{x + 1}{1 - x}

sin (15 0^{\circ} - x)

1 - sin (- x)

2 sin (x + 3 0^{\circ}) + 3 cos (x)

sin (\frac{- 7 x}{6})

sec^{2} (\frac{π}{2} + x)

What is tan(arctan(x)+pi/4) ?
The solution to tan(arctan(x)+pi/4) is (x+1)/(1-x)