Express [(1-sin2x)^0.5]÷[(1+sin2x)^0.5] in terms of tanx using the half angle t formula?

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Feb 15, 2018

Answer:

#=> (1-tan x) / (1+tan x)#

Explanation:

#sin (2x) = (2tan x)/(1+tan^2x)#

#sqrt((1-sin (2x)) / (1+sin(2x)))#

#=> sqrt((1- ((2tan x) / (1+tan^2 x)))/ (1+ ((2 tan x) / (1+tan^2theta))#

#=> sqrt(((1+tan^2 x-2tan x) / cancel(1+tan^2 x))/((1+tan^2 x-2tan x) / cancel(1+tan^2 x)))#

#=> sqrt((1-tan x)^2 / (1+tan x)^2)#

#=> (((1-tan x)/(1+tan x))^cancel2)^cancel(1/2)#

#=> (1-tan x) / (1+tan x)#

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