Trigonometric identities

Question

Use a common denominator to express the rational expression as a single term

 

(sinx)/(1+cosx) + (cosx)/(sinx)

 

the answer is cscx

Answer 1

   sinx            cosx

---------    +  ------------

1+cosx           sinx

 

       sin²x + cosx(1+cosx)

=   ---------------------------

          sinx(1+cosx)

 

      (sin²x+cos²x) + cosx

=   ---------------------------

          sinx(1+cosx)

 

             (1+cosx)

=   ---------------------------

         sinx(1+cosx)

 

                 1

=           --------      = cscx

              sinx