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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