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

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sodelete | Student, College Freshman | eNoter

Posted June 14, 2011 at 7:20 PM via web

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

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 14, 2011 at 7:27 PM (Answer #1)

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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

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giorgiana1976 | College Teacher | Valedictorian

Posted June 14, 2011 at 7:54 PM (Answer #2)

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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.

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lochana2500 | Student, Undergraduate | Valedictorian

Posted July 7, 2012 at 6:02 PM (Answer #3)

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tan 2x

= 2tanx / (1 - tan²x)

We know that tanx= √2

= 2√2 / [1-(√2)²]

= 2√2 / (1-2)

= 2√2 / -1

= -2√2

 

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