We'll use the following definitions of trigonometric identities to prove the statement:
[tex]tan(x)= \frac{sin(x)}{cos(x)} [/tex]
[tex]cot(x)= \frac{1}{tan(x)}= \frac{cos(x)}{sin(x)} [/tex]
With this, we start rewriting the left given expression:
[tex]cot(x)[cos(x)tan(x)+sin(x)]=[/tex]
[tex] \frac{cos(x)}{sin(x)}[cos(x) \frac{sin(x)}{cos(x)} +sin(x)]=[/tex]
[tex] \frac{cos(x)}{sin(x)}[sin(x) +sin(x)]= \frac{cos(x)}{sin(x)}[2sin(x)]=2cos(x) [/tex]
Hence, we have proven that the statement is true.
