prove the following trigonometric identity

Question

sinx÷ cscx + cosx÷ secx=1

Answer 1

sine = 1/cosecant

cosine = 1/secant

sinx/cscx = sinx/1/sinx = sin^2x

cosx/secx = cosx/1/cosx = cos^2x

sin^2x + cos^2x = 1

Answer 2

sin² x + cos² x = 1
              1
csc x = ------
            sin x
              1
sec x = ------
            cos x
~~~~~~~~~~~  
            1                       1 
sin x ÷ ------ + cos x ÷ ------ = 1
           sin x                 cos x 


sin x * sin x + cos x * cos x = 1

sin² x + cos² x = 1 

         1 = 1