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

User Tro
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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.
User Murat Mustafin
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