Question: If tan(A+B)=3 and tan(A−B)=31; 0°<A+B≤90°; A>B, find A and B.

Here, we are given that

tan(A+B)=3

tan(A−B)=31

0°<A+B≤90°

A>B

The most important part of this numerical is that we have to remember the values of tan for different angles, as shown in the table below

tan0°

tan30°

tan45°

tan60°

tan90°

0

31

1

3

Not defined

We know from the table above that, tan60°=3. So using this value in the 1st equation from given data:

tan(A+B)∴tan(A+B)∴A+B=3=tan60=60−−−(5)

Explanation for the above block:
Here we are comparing LHS with RHS. We can say that the equation tan (A+B) equates to √3 and tan 60 is √3 (you can find that in table).
So, this is only possible if A+B = 60 which satisfies this equation.

In the same manner, we know that, tan30°=31. So using this value in the 2nd equation from given data:

tan(A−B)=31∴tan(A−B)∴A−B=tan30=30−−−(6)

Adding equation (5) and equation (6), we get:

A+B=60A−B=30—————2A=90∴A=45°

Now, we can calculate the value of B by putting the value of A in either equation (5) or equation (6). Let's do it using equation (5):

A+B∴45+B∴B=15°=60=60

We can further confirm that our answer is correct by looking at equations (3) and equation (4) from the given data that:

0<AAnd so is 0<+B≤9060≤90

And,

A60>B>15

Hence, m∠A=60° and m∠B=15°

Suggested Notes:

15 cot A = 8 | Find the value of sin A and sec A | Trigonometry Numerical

PQ = 12cm and PR = 13cm | Find tan P - cot R | Trigonometry Numerical

cot θ = 7/8 | Find all other trigonometric ratios | Trigonometry Numerical

Trigonometry Formulas | sin θ, cos θ, tan θ, cosec θ, sec θ, cot θ | Trigonometry Basics

Suggested Notes:

15 cot A = 8 | Find the value of sin A and sec A | Trigonometry Numerical

PQ = 12cm and PR = 13cm | Find tan P - cot R | Trigonometry Numerical

cot θ = 7/8 | Find all other trigonometric ratios | Trigonometry Numerical

Trigonometry Formulas | sin θ, cos θ, tan θ, cosec θ, sec θ, cot θ | Trigonometry Basics

## Comments:

All comments that you add will await moderation. We'll publish all comments that are topic related, and adhere to our Code of Conduct.

Want to tell us something privately? Contact Us

## Post comment