Michael F.

asked • 01/26/18

Can't Solve -1-√3 * 1-√3 ------- ------ 1+√3 * 1-√3

I am doing sum and difference formulas with sin, cos, and tan. I am doing tan75 with the difference formula.
 
So tan 120-45
 
I have all the things found I just don't know how to multiply it by the denominators conjugate.
 
-1-√3 * 1-√3
-------  --------
1+√3 * 1-√3 
 
The answer key says 2+√3. I just need to show my work. I'm a junior in trig.

David W.

tutor
Something is not right.
 
(-1 -√3)/(1 + √3) = -1(1 + √3)/(1 + √3) = -1
 
If you typed it correctly, the teacher made an error.
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01/26/18

Bobosharif S.

(√3-1)2=(√3)2-2*1*√3+(-1)2=3-2√3+1
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01/28/18

2 Answers By Expert Tutors

By:

Bobosharif S. answered • 01/26/18

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tan[75]=tan[120-45]=(tan(120)-tan(45))/(1+tan(120)tan(45))=
=(√3-1)/(√3+1)=
=[(√3-1)(√3-1)]/[(√3+1)(√3-1)]=[3-2√3+1]/[3-1]=
=(4-2√3)/2=2-√3.
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Michael F.

This is very helpful! I am stuck on one part primarily though. When you do [3-2√3+1]/[3-1]=
=(4-2√3)/2=2-√3, I am not sure where the two or the four is coming from. Sorry! I just want to understand this. Math is my weak point because I miss little things here and there. Thanks!
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01/27/18

Bobosharif S.

Multiply both numerator and  denominator of (√3-1)/(√3+1) by (√3-1)
Numerator: (√3-1)(√3-1)=(√3-1)2 =(√3)2-2√3+(-1)2=3-2√3+1=4-2√3.
 
 
 
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01/28/18

Bobosharif S.

Denominator:(√3+1)(√3-1)=(√3)2-12=3-1=2.
 
Now combine
(4-2√3)/2=2-√3.
 
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01/28/18

Bobosharif S.

I answered it yesterday, nut buy  some reasons, it didn't go through.
I hope now it is clear. If not ask.
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01/28/18

Michael F.

Thank you so much! This has helped me immensely. Now I see what I was missing.
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01/28/18

Michael F.

Actually I need help with one little part. On the numerator part, (√3)2-2√3+(-1)2, where is the bold part coming from. Sorry!
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01/28/18

Bobosharif S.

We use formula (a-b)2=a2-2ab+b2
(√3-1)2=(√3)2-2*1*√3+(-1)2=3-2√3+1
 
 
 
 
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01/28/18

Bobosharif S.

We use (a-b)2=a2-2ab+b2. So
(√3-1)2=(√3)2-2*1*√3+(-1)2=3-2√3+1.
 
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01/28/18

Bobosharif S.

We use (a-b)2=a2-2ab+b2 So
(√3-1)2=(√3)2-2*1*√3+(-1)2=3-2√3+1
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01/28/18

Bobosharif S.

We use (a-b)^2=a^2-2ab-b^2. So, (√3-1)^2=(√3)^2-2*1*√3+(-1)^2=
=3-2√3+1.
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01/28/18

Bobosharif S.

Use formula for square of sum (difference): (a-b)^2
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01/28/18

Michael F.

Ohh! Ok, thank you so much! That is all I needed help with. You are a lifesaver, :D
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01/28/18

Bobosharif S.

You are welcome!
=(√3-1)2=(√3)2-2*1*√3+(-1)2=3-2√3+1=4-2√3
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01/28/18

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