# Given tan x = square root 2, write tan (2x) numerically.

*print*Print*list*Cite

### 3 Answers

We know that tan 2x = 2*tan x/[1-(tan x)^2]

tan x = sqrt 2, substitute this in the expansion for tan 2x

tan 2x = 2* sqrt 2/[1 - (sqrt 2)^2]

=> 2*sqrt 2/(1 - 2)

=> -2*sqrt 2

**The value of tan 2x = -2*sqrt 2**

### User Comments

tan 2x

= 2tanx / (1 - tan²x)

We know that tanx= √2

= 2√2 / [1-(√2)²]

= 2√2 / (1-2)

= 2√2 / -1

= -2√2

We'll apply double angle identity:

tan 2x = tan (x+x) = (tanx + tan x)/[1-(tan x)^2]

tan 2x = 2tanx/[1-(tan x)^2] (1)

Since tan x = sqrt2, we'll replace tan x by sqrt 2 in (1):

tan 2x = 2sqrt2/[1-(sqrt2)^2]

tan 2x = 2sqrt2/-1

tan 2x = -2sqrt2

The requested numerical value of tan 2x is: tan 2x = -2sqrt2.