Simplify the expression. 5 -tan(?)/ 5csc(?) - sec (?)

Question

I know you are supposed to us the trig identities, but I have know idea where to even begin.

Answer 1

(5 - tanθ)/(5cscθ - secθ) = [5 - sinθ/cosθ)]/[5/sinθ - 1/cosθ]

 

                       = [(5cosθ - sinθ)/cosθ]/[(5cosθ - sinθ)/(sinθcosθ)]

 

                       = [(5cosθ - sinθ)/cosθ][(sinθcosθ)/(5cosθ - sinθ)

 

 Cancelling out cosθ and 5cosθ - sinθ, the expression simplifies to sinθ.

Answer 2

 

If x=?                                                                                5Cosx - Senx 

                                                                                        ____________

                                                    5-Senx/Cosx                          Cosx                        (5Cosx-Senx) Senx.Cosx

 5-tanx/5Cscx-Secx              =     ______________       = __________________ =    ____________________________

                                                 5/Senx  -   1/Cosx      

                                                                                          5Cosx-Senx                    (5Cosx-Senx) Cosx

                                                                                          ___________

                                                                                          Senx Cosx

 

 

Simplifying:             Senx.