Question

It’s PreCal I just need a method to solve it

Answer 1

see explanation

Explanation:

Using the identities

tanx =
`(sinx)/(cosx)` , cotx =
`(cosx)/(sinx)`

Consider the left side

`(tanx)/(tanx+cotx)`

=
`((sinx)/(cosx) )/((sinx)/(cosx)+(cosx)/(sinx) )`

=
`((sinx)/(cosx) )/((sin^2x+cos^2x)/(cosxsinx) )`

=
`((sinx)/(cosx) )/((1)/(cosxsinx) )`

=
`(sinx)/(cosx)` ×
`(cosxsinx)/(1)` ← cancel cosx on numerator/ denominator

= sin²x

= right side