A simplified version of the expression 2sin theta (cos theta)(cot theta) is... I tried to use the reciprocal of cotangent theta and then cancle out cos theta, being left with 2sin theta and sin theta but I was wrong. May someone help me?

Question

terenzreignz · Answer

Depends what you mean by simplified

anonymous · Answer

Well my options are A.) sin ^2 theta, B.) 2cos^2 theta, C.) cos^2 theta. I want to say it's A.) but I'm not entirely sure. Before I had written 2sin theta(csc theta) but I was marked incorrect. I'm not sure how to explain what it means by simplify.

ash2326 · Answer

$$2 \sin \theta \times \cos \theta \cot \theta$$
We know $\large \cot \theta =\frac {\cos \theta}{\sin \theta}$
so we have now
$$2 \sin \theta \times \cos \theta \times \frac {\cos \theta}{\sin \theta}$$

Now we have
$$2 \cancel{\sin \theta} \times \cos \theta \times \frac {\cos \theta}{\cancel{\sin \theta}}$$
What do you get now?

anonymous · Answer

Would it be cos^2?

ash2326 · Answer

uh-huh, you're missing the 2 !

anonymous · Answer

I'm sorry, what do you mean? (:

anonymous · Answer

Like 2cos^2?

ash2326 · Answer

Yeah:] you're correct

anonymous · Answer

Oh, thank you! I really appreciate that you wrote the steps out (: Makes much more sense!

ash2326 · Answer

you're welcome:D