Question #54eff

1 Answer
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