Question #54eff

1 Answer
Y
May 15, 2017

Use definition of tangent and Pythagorean's identity
Answer: #sin^2x#

Explanation:

Simplify #1-sin^2x/tan^2x#

Note that #tanx=sinx/cosx#

We can substitute #tan^2x=sin^2x/cos^2x#
#=1-sin^2x/(sin^2x/cos^2x)#
#=1-sin^2x*cos^2x/sin^2x#
#=1-cos^2x#

Consider the Pythagorean identity:
#sin^2x+cos^2x=1#
we can rearrange to get:
#sin^2x=1-cos^2x#

Therefore,
#=sin^2x#

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