Question

Question #54eff

Answer 1

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`