Simplify: sin^2x - cos^2x / 1-tan^2x ?

1 Answer
Øko
Apr 12, 2018

#(sin^2(x)-cos^2(x))/(1-tan^2(x))=-cos^2(x)#

Explanation:

#(sin^2(x)-cos^2(x))/(1-tan^2(x))#

#=(sin^2(x)-cos^2(x))/(1-sin^2(x)/cos^2(x))#

#=((sin^2(x)-cos^2(x))cos^2(x))/((1-sin^2(x)/cos^2(x))cos^2(x))#

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

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

#=-cos^2(x)#

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