Help simplfying a trig identity

sin(pi/4+x)-cos(pi/4+x)
So far I have: =(sinpi/4)(cosx)-(cospi/4)(cosx)
=(sqrt2/2)(cosx)-(sqrt2/2)(cosx)
...and now I'm stuck :/
The answer is suppossed to be sqrt2sinx

I can see your problem already....

In order to break up sin(pi/4+x) and cos(pi/4+x) you need to use the following identity.

sin(x+y) = sinxcosy + cosxsiny
cos(x+y) = cosxcosy - sinxsiny

So to split up sin(pi/4+x), this would be sin(pi/4)cos(x) + cos(pi/4)sin(x)

And cos(pi/4+x) would be cos(pi/4)cos(x) - sin(pi/4)sin(x)

Now you need to put them together....

sin(pi/4)cos(x) + cos(pi/4)sin(x) - [cos(pi/4)cos(x) - sin(pi/4)sin(x)]

don't forget brackets(need to distribute the -)


sin(pi/4)cos(x) + cos(pi/4)sin(x) - cos(pi/4)cos(x) + sin(pi/4)sin(x)

You had the sin(pi/4) and the cos(pi/4) already so i will use your numbers...

(sqrt2)/2 * cos(x) + (sqrt2)/2 * sin(x) - (sqrt2)/2 * cos(x) + (sqrt2)/2 * sin(x)

Combine like terms....
Notice the cos(x) cancels out since it is being subtracted.

so we have [(sqrt2)/2+(sqrt2)/2] sin(x)

by adding the fractions you have [2(sqrt2)/2] * sin(x)

The 2's cancel and therefore you have (sqrt2) * sin(x) your answer

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Sorry about length it is hard to explain over the internet like this so it was going to be lengthy.

yes