Question

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

Answer 1

Used Sum and difference Angle formulas for sine and cosine to simplify

Answer 2

So 2sinAcosB=sin(A+B)+sin(A-B)

Answer 3

But how the question sin and cos become sin and sin in the forumla?

Answer 4

where'd you get that formula.

Answer 5

My tudor

Answer 6

Is it incorrect?

Answer 7

It doesn't look correct as written

Answer 8

What's the correct formula?

Answer 9

http://regentsprep.org/Regents/math/algtrig/ATT14/formulalesson.htm

Answer 10

Ohh, right

Answer 11

So what formula do I use?

Answer 12

Do I work with sin (45-x) separately and then cos (45-x) separately?

Answer 13

Yep, I understood that part

Answer 14

I subbed in the values and got this:

Answer 15

(sin45cosx-cos45sinx) (cos45cosx+sin45sinx)

Answer 16

You should know what Sin 45 and cos ( 45)

Answer 17

Sin 45 is rt2/2

Answer 18

And cos 45 is rt2/3

Answer 19

They're both sqrt(2)/2

Answer 20

What about the x ?

Answer 21

You don't need to Know What x ls. You're simplifying an expression not solving an equation.

Answer 22

Am I doing this wrong?

Answer 23

Yes

Answer 24

Okay

Answer 25

How do I further simplify this?

Answer 26

Algebraically

Answer 27

So that becomes

Answer 28

(rt2/2)^2 x (cosx-sinx)(cosx+sinx)

Answer 29

Just try to work on it and post your simplification

Answer 30

= 1/2 x (cosx-sinx)(cosx+sinx)

Answer 31

I don't know how to further simplify

Answer 32

There's no x after 1/2

Answer 33

Oh that's a multiplication sign

Answer 34

= 1/2(cosx-sinx)(cosx+sinx)

Answer 35

That's a difference of two squares

Answer 36

correct

Answer 37

=1/2(cosx-sinx)^2

Answer 38

Not written correctly

Answer 39

Do you want to try to correct your own Mistake?

Answer 40

Is it 1/2 cosx^2-sin^2 ?

Answer 41

That's better

Answer 42

Yep

Answer 43

Ok, how do I further simplify?

Answer 44

sin(×) is the primitive trig expression So express the simplification in terms Of sine.

Answer 45

?

Answer 46

What do you mean?

Answer 47

Do you know the Pythagorean identity?

Answer 48

Yes

Answer 49

sin^2x+cos^2x=1

Answer 50

Could you please give me the completed working out, I'm a bit short on time

Answer 51

Isolate cos^2 x

Answer 52

We're almost done.

Answer 53

And then..?

Answer 54

substitute cos ^2x with its equivalent expression then finish simplifying

Answer 55

Ok thank you so much

Answer 56

By the way,

Answer 57

Yes?