Question

how to simplify (cosx+sinx)(cos-x-sin-x)

Answer 1

cos(-x) = cosx

sin(-x) = -sinx

Start from there.

Answer 2

$$\begin{align*}(\cos x+\sin x)(\cos (-x)-\sin (-x))&=(\cos x+\sin x)(\cos x+\sin x)\\&=\cos^2x+2\sin x\cos x+\sin^2x\\&=\sin 2x\end{align*}$$

Answer 3

It makes sense until the last line of the equation... how did you get from the second to last line to the last line?
Thanks so much. This is so helpful.

Answer 4

@oldrin.bataku i think you missed the 1.

http://www.mathwords.com/t/trig_identities.htm

\[\Large \cos^2x+2\sin x\cos x+\sin^2x\ \] rearrange the terms
\[\Large \cos^2 x+\sin^2 x + 2\sin x \cos x\]
Remember that cos^2x+sin^2x = 1, so:
\[\Large 1 + 2\sin x \cos x\]

and 2sinxcosx = sin2x, so
\[\Large 1 + \sin 2x\]

Answer 5

This makes so much more sense! Thank you!

Answer 6

@agent0smith oops right :-)