Question

How can you prove sinθ+cotθ(both over)/cosθ = tanθ+cscθ?

Answer 1

Verified, step by step below...

Explanation:

`(sinθ+cotθ)/cosθ = tanθ+cscθ`

1. Split the numerator
   `sintheta/costheta+cottheta/costheta= tantheta+csctheta`

2. Apply the quotient identity:`tantheta= sintheta/costheta`
   `tantheta+cottheta/costheta= tantheta+csctheta`

3. Apply the quotient identity: `cottheta= costheta/sintheta`|
   `tantheta+(costheta/sintheta)/costheta= tantheta+csctheta`

4. Simplify
   `tantheta+(cancelcostheta/sintheta)*1/cancelcostheta= tantheta+csctheta`

`tantheta+1/sintheta= tantheta+csctheta`

1. Apply the reciprocal identity: `1/sintheta= csctheta`
   `tantheta+csctheta= tantheta+csctheta`