Question

Simplify Using identities. CosB*SinB/Sin^2B-Cos^2B

Answer 1

Try to use Identities:

\[2\sin(x) \cos(x) = \sin(2x)\]
\[\cos^2(x) - \sin^2(x) = \cos(2x)\]

Answer 2

To use this efficiently, multiply and divide by \(-2\)..

Answer 3

The 2B is actually separate. B is an angle. and Sin^2 and Cos^2. After simplifying it must be equal to cotB/1-cot^2 B. And I'm unable to simplify it that far

Answer 4

@waterineyes

Answer 5

Yes I know that..

Answer 6

You mea\[\frac{\cos(x)\sin(x)}{\sin^2(x) - \cos^2(x)}\]n this:

Answer 7

I mean that is your question no?

Answer 8

So multiply and divide by \(-2\) :

\[\frac{-2 \cos(x) \sin(x)}{2(\cos^2(x) - \sin^2(x))} \implies \frac{-\sin(2x)}{2\cos(2x)} \implies \color{green}{\frac{-1}{2}\tan(2x)}\]

Answer 9

In denominator, I have used - sign to brackets, so cosine term will come first and then sine..

Answer 10

Yes is. -1/2 tan(2X) your simplified answer?

Answer 11

I have just calculated it, you should check now whether it is simplified or not.. :)

Answer 12

The final simplified solution is supposed to be cotB/1-cot^2 B