Pre-cal: Simplify using sum and difference identities

calc1

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I'm not able to get anywhere with this problem. I've tried factoring, multiplying, regrouping, but I cannot find the identities. Thanks for looking at this.

(cos2b-sin2b)/2sinbcosb
 
I'm not able to get anywhere with this problem. I've tried factoring, multiplying, regrouping, but I cannot find the identities. Thanks for looking at this.

(cos2b-sin2b)/2sinbcosb
Have you been studying double-angle formulas? Or could you look up sum-of-angle formulas sine and cosine of (A + B) when A=B?
 
I'm not able to get anywhere with this problem. I've tried factoring, multiplying, regrouping, but I cannot find the identities. Thanks for looking at this.

(cos2b-sin2b)/2sinbcosb

Please tell us which sum and difference identities that you have referred to in your title of the post.
 
Have you been studying double-angle formulas? Or could you look up sum-of-angle formulas sine and cosine of (A + B) when A=B?

No. Double-angle identities are in our next section. I have not seen anything about when A=B. This is an online course and the material is scant and a bit disjointed.

So . . .

= cos2b/sin2b = cot2b?
 
No. Double-angle identities are in our next section. I have not seen anything about when A=B. This is an online course and the material is scant and a bit disjointed.

So . . .

= cos2b/sin2b = cot2b?

Correct!
 
I'm not able to get anywhere with this problem. I've tried factoring, multiplying, regrouping, but I cannot find the identities. Thanks for looking at this.

(cos2b-sin2b)/2sinbcosb

quote_icon.png
Originally Posted by calc1
No. Double-angle identities are in our next section. I have not seen anything about when A=B. This is an online course and the material is scant and a bit disjointed.

So . . .

= cos2b/sin2b = cot2b?

I said correct a little too hastily!

If your problem was;

Simplify:

(cos2b-sin2b)/(2sinbcosb)

and if your answer was

= cos(2b)/sin(2b) = cot(2b)

Then only the response is correct.

Notice the grouping symbols - () - for correctness!
 
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