SOLUTION: If tan(A+B) = 1/7 and tanA = 3, find without using tables, the value of tanB.

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Question 1134822: If tan(A+B) = 1/7 and tanA = 3, find without using tables, the value of tanB.
Found 2 solutions by mathsolverplus, ikleyn:
Answer by mathsolverplus(88) About Me  (Show Source):
You can put this solution on YOUR website!
Use the formula:
tan%28a%2Bb%29+=+%28tan%28a%29%2Btan%28b%29%29%2F%281-tan%28a%29tan%28b%29%29
+%281%2F7%29+=+%283%2Btan%28b%29%29%2F%281-3tan%28b%29%29+
Let tan(b) = x,
1%2F7+=+%283%2Bx%29%2F%281-3x%29
1%2F7-3x%2F7+=+3%2Bx
-10x%2F7=20%2F7
x=-2
Therefore, tan(b)=-2

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Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

            The way on how the other tutor resolved this problem/question,  is formally correct,

            but this problem can be solved in  MUCH  EASIER  way.

            What is even more important, this problem  IS  DESIGNED  and  IS  INTENDED  to be solved by the other,  more simple way.

            See my solution below. 


The identity  (A + B) - A = B  directly instructs and prescribes you to use the formula of difference for tangent function,

which originally has the form


    tan(x - y) = %28tan%28x%29-tan%28y%29%29%2F%281%2Btan%28x%29%2Atan%28y%29%29


Using this formula, you should take x = A+B, y = A  to get


    tan(B) = tan((A+B) -A) = %28tan%28A%2BB%29+-+tan%28A%29%29%2F%281+%2B+tan%28A%2BB%29%2Atan%28B%29%29 = 


        now substitute the given values  tan(A+B) = 1%2F7  and  tab(B) = 3  to get


  = %28%281%2F7+-+3%29%29%2F%28%281+%2B+%281%2F7%29%2A3%29%29 = %28%281-3%2A7%29%2F7%29%2F%28%287%2B3%29%2F7%29 = %28%28-20%2F7%29%29%2F%28%2810%2F7%29%29 = -20%2F10 = -2.    ANSWER


In this way, the problem is just SOLVED.


Notice, that this solution  DOES  NOT  REQUIRE  reducing the problem to some equation and solving it.

It only requires to make one line simple calculations based on well known Trigonometry formula.

If my solution seems complicated to you from the first glance  (although it is as simple as possible),

I will repeat it one more time,  by omitting accompanying explanations - they are needed only for the first time: 

    tan(B) = tan((A+B) -A) = %28tan%28A%2BB%29+-+tan%28A%29%29%2F%281+%2B+tan%28A%2BB%29%2Atan%28B%29%29 = %28%281%2F7+-+3%29%29%2F%28%281+%2B+%281%2F7%29%2A3%29%29 = %28%281-3%2A7%29%2F7%29%2F%28%287%2B3%29%2F7%29 = %28%28-20%2F7%29%29%2F%28%2810%2F7%29%29 = -20%2F10 = -2.

This one line version is how the solution should be and must be presented when you know the way on how to solve it . . .


Once again: my post is the way on how this problem expected and intended to be solved.

The other's tutor solution is a wrong approach to the problem.