Cot x/2=-k then tan x=?

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Answer 1 · 2018-05-20T07:40:55

#color(maroon)(tan x = (2k)/((1+k)(1-k))#

#cot (x/2) = -k, tan x = ?#

#tan (x/2) = -(1/k)#

#color(green)(tan x = (2 tan(x/2)) / (1 - tan^2 (x/2))#, identity

Substituting for #tan (x/2) = -1/k#,

#tan x = (-2/k) / (1-(-1/k)^2)#

#tan x = (2/k) / ((1/k^2) - 1)#

#tan x = (2/k) / ((1-k^2)/k^2)#

#color(maroon)(tan x = (2k)/((1+k)(1-k))#

Answer 2 · 2018-05-20T07:42:21

#tanx=(-2k)/(k^2-1)#

We know that,

#color(blue)(tantheta=(2tan(theta/2))/(1-tan^2(theta/2))...to(1)# [half angle formula]
Now,given that,

#cot(x/2)=-k=>tan(x/2)=-1/k...to(2)#

Using #(1)#

#tanx=(2tan(x/2))/(1-tan^2(x/2)#

#=>tanx=(2(-1/k))/(1-(-1/k)^2)...toApply(2)#

#=>tanx=(-2/k)/(1-1/(k^2))#

#=>tanx=(-2/k)/((k^2-1)/k^2)#

#=>tanx=(-2k)/(k^2-1)#