What is the right way of simplifying this trigonometric expression and why?Problem: c o s A s i n A − c o s A c o s A s i n A + c o s A sol1: = c o s A ( 1 s i n A − 1 ) c o s A ( 1 s i n A + 1 ) = ( 1 s i n A − 1 ) ( 1 s i n A + 1 ) = c o s e c A − 1 c o s e c A + 1 sol2: = c o s A − s i n A c o s A c o s A + s i n A c o s A B y ÷ c o s A = 1 − c o s e c A 1 + c o s e c A

Question

What is the right way of simplifying this trigonometric expression and why?Problem:                              c          o          s          A                          s          i          n          A                    −      c      o      s      A                                c          o          s          A                          s          i          n          A                    +      c      o      s      A      sol1:  =            c      o      s      A              (                  1                      s            i            n            A                          −        1        )                    c      o      s      A              (                  1                      s            i            n            A                          +        1        )              =            (              1                  s          i          n          A                    −      1      )              (              1                  s          i          n          A                    +      1      )        =            c      o      s      e      c      A      −      1              c      o      s      e      c      A      +      1      sol2:  =            c      o      s      A      −      s      i      n      A      c      o      s      A              c      o      s      A      +      s      i      n      A      c      o      s      A        B  y  ÷  c  o  s  A  =            1      −      c      o      s      e      c      A              1      +      c      o      s      e      c      A

benedictazk · Accepted Answer

Your last step is incorrect.                    1        −        sin        ⁡        A                    1        +        sin        ⁡        A              =                    csc        ⁡        A        −        1                    csc        ⁡        A        +        1

juanberrio8a · Accepted Answer

your sol2 should be:  =            c      o      s      A      −      s      i      n      A      c      o      s      A              c      o      s      A      +      s      i      n      A      c      o      s      A      dividing by cosA gives,  =                              c          o          s          A                          c          o          s          A                    −                        s          i          n          A          C          o          s          A                          c          o          s          A                                              c          o          s          A                          c          o          s          A                    +                        s          i          n          A          c          o          s          A                          c          o          s          A                    the result is ,  =            1      −      s      i      n      A              1      +      s      i      n      A      focus on your mistake.

What is the right way of simplifying this trigonometric expression and why? Problem:

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