Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How would I prove the following two trigonometric identity.

$$\cot A\sin 2A=1+\cos 2A$$

This is my work so far

$$\frac{\cos A}{\sin A}(2\sin A \cos A)=1+\cos 2A$$

I am not sure what I would do next to make them equal.

share|cite|improve this question
I would but it wont let me click the checkmark. – Fernando Martinez Jul 26 '12 at 17:27
up vote 1 down vote accepted

\begin{eqnarray*} cotAsin2A=\frac{cosA}{sinA}(2sinAcosA)=cosA(2cosA)=2cos^2A=1+cos2A \end{eqnarray*}

This should be everything.

share|cite|improve this answer

After cancellation, you've got $2\cos^2A$ on the left. One of your double angle identities will get you the rest of the way.

share|cite|improve this answer
Can you give a hint of which one is it 2cos^2-1? – Fernando Martinez Jul 26 '12 at 17:24
Precisely that one. That will let you rewrite $2\cos^2 A$ in terms of $\cos(2A)$--namely, $2\cos^2 A=1+\cos(2A)$, as desired. – Cameron Buie Jul 26 '12 at 17:34

$$ \frac{\cos A}{\sin A}(2\sin A \cos A) = 2\cos^2 A \\ $$ Then use the identity $2\cos^2 A = \cos(2A) + 1$ from this link here.

share|cite|improve this answer
Oh I see I have a website with the double angle indemnities yet they can be written in more ways than just 2cos^2A-1=cos(2A). – Fernando Martinez Jul 26 '12 at 17:42

$$\cot (a) \cdot \sin(2a) = 1 + 1 - 2\sin^2(a)$$

$$=\frac{\cos (a)}{\sin (a)} \cdot 2\sin(a)\cos(a) = 2(1-\sin^2(a))$$

$$=2\cos^2(a) = 2\cos^2(a)$$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.