Question

Prove or disprove that 2cosx is the same as cotx(cosxtanx+sinx)

Answer 1

We'll use the following definitions of trigonometric identities to prove the statement:


`tan(x)= (sin(x))/(cos(x))`

`cot(x)= (1)/(tan(x))= (cos(x))/(sin(x))`

With this, we start rewriting the left given expression:


`cot(x)[cos(x)tan(x)+sin(x)]=`

`(cos(x))/(sin(x))[cos(x) (sin(x))/(cos(x)) +sin(x)]=`

`(cos(x))/(sin(x))[sin(x) +sin(x)]= (cos(x))/(sin(x))[2sin(x)]=2cos(x)`

Hence, we have proven that the statement is true.