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#1 2018-01-29 03:27:41

Monox D. I-Fly
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From: Indonesia
Registered: 2015-12-02
Posts: 1,047

[ASK] Trigonometric Equation

If 0 < x < 90, what is the solution of tan(2x - 5) = cot(x + 5)?
I got stuck in tan(2x - 5)tan(x + 5) = 1. What should I do after that?


Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away. May his adventurous soul rest in peace at heaven.

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#2 2018-01-29 03:39:45

Alg Num Theory
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Registered: 2017-11-24
Posts: 57
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Re: [ASK] Trigonometric Equation

Oops, that does not work. If tanAtanB = 1, then the denominator in the formula for tan(A+B) is 0.

Sorry, back to the drawing board …

Last edited by Alg Num Theory (2018-01-29 03:45:41)

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#3 2018-01-29 04:43:53

bob bundy
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Registered: 2010-06-20
Posts: 8,236

Re: [ASK] Trigonometric Equation

try using:

cos(A-B) + cos(A+B) = 2 cos(A) . cos(B)

A = 2x-5 and B = x+5

and a similar formula with a minus sign.

Bob


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You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#4 2018-01-29 12:44:27

Monox D. I-Fly
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From: Indonesia
Registered: 2015-12-02
Posts: 1,047

Re: [ASK] Trigonometric Equation

What does it have to do with cos? The questions are tan and cot.


Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away. May his adventurous soul rest in peace at heaven.

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#5 2018-01-29 20:45:53

bob bundy
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Registered: 2010-06-20
Posts: 8,236

Re: [ASK] Trigonometric Equation

hi Monox D. I-Fly

Sorry my post was too brief.  I was in a hurry as I had to go out.  Here's some more detail:

note:

Let A = 2x-5 and B = x+5  => A-B = x - 10  and A+B = 3x

The two trig. formulas that will help are

and

so the equation becomes:

I'll leave you to finish this. smile

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#6 2018-01-30 03:23:56

Alg Num Theory
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Registered: 2017-11-24
Posts: 57
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Re: [ASK] Trigonometric Equation

I have an idea: if tanA·tanB = 1, then A+B must be an odd multiple of 90°. Example:

and 30° + 60° = 90°.

In the OP’s example, 0 < x < 90°, so 0 < (2x + 5) + (x − 5) = 3x < 270° ⇒ x = 90°.

PS: Check: tan(175°) = 1/tan(95°) so I think I’m on the right track. smile

Last edited by Alg Num Theory (2018-01-30 03:27:23)

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#7 2018-01-30 14:24:40

Monox D. I-Fly
Member
From: Indonesia
Registered: 2015-12-02
Posts: 1,047

Re: [ASK] Trigonometric Equation

Huh? You got 90°? What I got was 30°.


Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away. May his adventurous soul rest in peace at heaven.

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#8 2018-01-30 16:20:57

Alg Num Theory
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Registered: 2017-11-24
Posts: 57
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Re: [ASK] Trigonometric Equation

Sorry, I meant to say 3x = 90°, so yes, x = 30°.

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