Thread: What would be the value?

1. 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) = ??

2. Re: What would be the value?

Start with the expansion for tan(A+B) and see what you can do.

3. Re: What would be the value?

A+B=225
A+B=180+45
(1+tanA)(1+tanB)
=(1+tan180)(1+tan45)
=(1+0)(1+1)
Ans. 2 [tan 180=0, tan45=1]

4. 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

5. 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, $(1+tanA)(1+tanB)=2$

6. Re: What would be the value?

It is better that we give hint / direction rather than spoon feeding in the interest of the learner

7. 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".