How do you simplify #(1-cos^4x-sin^4x)/(sin^4x-2sin^2x+1)#?

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Answer 1 · 2018-05-07T11:54:43

#2 tan^2(x)#

#"put "y = sin^2(x)#
#=> cos^2(x) = 1 - y , " as "sin^2(x)+cos^2(x)=1.#
#"Then we have"#

#(1 - (1 - y)^2 - y^2)/(y^2 - 2 y + 1)#

#= (2 y - 2 y^2)/(y - 1)^2#

#= 2 y(1 - y)/(y-1)^2#

#= 2 y /(1 - y)#

#= 2 sin^2(x) / cos^2(x)#

#= 2 tan^2(x)#