Simplify sin(45-x)cos(45-x)

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Simplify sin(45-x)cos(45-x)

Mathematics
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Used Sum and difference Angle formulas for sine and cosine to simplify
So 2sinAcosB=sin(A+B)+sin(A-B)
But how the question sin and cos become sin and sin in the forumla?

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Other answers:

where'd you get that formula.
My tudor
Is it incorrect?
It doesn't look correct as written
What's the correct formula?
http://regentsprep.org/Regents/math/algtrig/ATT14/formulalesson.htm
Ohh, right
So what formula do I use?
Do I work with sin (45-x) separately and then cos (45-x) separately?
Yep, I understood that part
I subbed in the values and got this:
(sin45cosx-cos45sinx) (cos45cosx+sin45sinx)
You should know what Sin 45 and cos ( 45)
Sin 45 is rt2/2
And cos 45 is rt2/3
They're both sqrt(2)/2
What about the x ?
You don't need to Know What x ls. You're simplifying an expression not solving an equation.
Am I doing this wrong?
Yes
Okay
How do I further simplify this?
Algebraically
So that becomes
(rt2/2)^2 x (cosx-sinx)(cosx+sinx)
Just try to work on it and post your simplification
= 1/2 x (cosx-sinx)(cosx+sinx)
I don't know how to further simplify
There's no x after 1/2
Oh that's a multiplication sign
= 1/2(cosx-sinx)(cosx+sinx)
That's a difference of two squares
correct
=1/2(cosx-sinx)^2
Not written correctly
Do you want to try to correct your own Mistake?
Is it 1/2 cosx^2-sin^2 ?
That's better
Yep
Ok, how do I further simplify?
sin(×) is the primitive trig expression So express the simplification in terms Of sine.
?
What do you mean?
Do you know the Pythagorean identity?
Yes
sin^2x+cos^2x=1
Could you please give me the completed working out, I'm a bit short on time
Isolate cos^2 x
We're almost done.
And then..?
substitute cos ^2x with its equivalent expression then finish simplifying
Ok thank you so much
By the way,
Yes?

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