Using trigonometric identities, transform the left side of the equation into the right side:
tan(x)cot(x) = 1

Question

Using trigonometric identities, transform the left side of the equation into the right side: 
tan(x)cot(x) = 1

***[isuru]*** · Answer

Hi,
        cot(x) is the reciprocal of tan(x) which means,
                                 cot(x) = 1/tan(x)
            
So let's keep it in our mind and move to the question
                tan(x) * cot(x) = 1
             L.H.S = tan(x) * cot(x)    [ let's substitute cot(x) = 1/tan(x) for cot(x) ; ]
                      = tan(x) * 1/tan(x)
                      = tan(x)/tan(x)
                      = 1
                      = R.H.S

   That's it!