hiiii,

try to answer the simple trigonometry question.

If A+B = 225 then what would be (1+tan A)(1+tan B) = ??

Source:- If A+B = 225 then what would be (1+tan A)(1+tan B) = ??

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- Jun 15th 2016, 11:01 PM #1

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## What would be the value?

**hiiii,**

try to answer the simple trigonometry question.

If A+B = 225 then what would be (1+tan A)(1+tan B) = ??

Source:- If A+B = 225 then what would be (1+tan A)(1+tan B) = ??

- Jun 16th 2016, 12:35 AM #2

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- Jul 19th 2016, 03:12 AM #3

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- Jul 19th 2016, 03:42 AM #4

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## Re: What would be the value?

There are some problems here.

1) Both abhik143 and garfieldmorse were naughty and did not include degree marks. Without degree marks, we are to assume that the angle is in radians. So

tan 180 ≈ 2.339, not 0. (*180 radians*)

tan 180° = 0. (*180 degrees*)

2) Shouldn't the original question include the restriction that A ≠ 90° or B ≠ 90°? Otherwise, (1 + tan A)(1 + tan B) can't be evaluated.

3) I don't think that we can just say that A = 180° and B = 45°. Let A = 100° and B = 125°, for example, and you'll get the same answer for (1 + tan A)(1 + tan B).

I think a better way to solve this would be to do the following:

$\displaystyle A + B = 225^{\circ}$

$\displaystyle tan(A + B) = tan(225^{\circ})$

$\displaystyle \frac{tan A + tan B}{1 - tan A \: tan B} = 1$

Multiply both sides by the denominator:

$\displaystyle tan A + tan B = 1 - tan A \: tan B$

$\displaystyle tan A + tan B + tan A \: tan B = 1$

$\displaystyle 1 + tan A + tan B + tan A \: tan B = 2$

Factor the left side:

$\displaystyle (1 + tan A)(1 + tan B) = 2$

01

- Oct 3rd 2016, 03:35 AM #5

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## Re: What would be the value?

$(1+tanA)(1+tanB)=1+tanA+tanB+tanAtanB ........(1)$

Given : $A+B=225$

taking tan on both the sides

$tan(A+B)=tan(225)$

$tan(A+B)=tan(180+45)$

$tan(A+B)=1 ........(2)$

We know, $tan(A+B)=\dfrac{tanA+tanB}{1-tanAtanB}$

put the value of tan(A+B) from equation (2)

$1=\dfrac{tanA+tanB}{1-tanAtanB}$

$1-tanAtanB=tanA+tanB$

$1=tanA+tanB+tanAtanB ........(3)$

put the value of $tanA+tanB+tanAtanB$ froam equation (3) into equation (1)

$(1+tanA)(1+tanB)=1+1$

Thus, $(1+tanA)(1+tanB)=2$

- Oct 6th 2016, 10:50 AM #6

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- Oct 6th 2016, 12:12 PM #7

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## Re: What would be the value?

**yeongil**: Your point is perfectly valid, but for the question to make any sense (for it to be a well posed question) it cannot matter what choice we make for $\displaystyle A$ and $\displaystyle B$, thus**garfieldmorse**'s suggestion is perfectly justifiable with the condition "if an answer exists, it is 2".