anonymous
  • anonymous
Simplify sin(45-x)cos(45-x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Hero
  • Hero
Used Sum and difference Angle formulas for sine and cosine to simplify
anonymous
  • anonymous
So 2sinAcosB=sin(A+B)+sin(A-B)
anonymous
  • anonymous
But how the question sin and cos become sin and sin in the forumla?

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

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