Question

if tan(a-b)=1/root 3,tan (a+b)=root 3,find a and b

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Answer 1

Yo!

Here's the answer!

Given:

Tan (a-b)= 1/√3 .....(1)

And Tan (a+b)= √3 ...(2)

We know that,

Tan 1/√3 is 30°

And Tan √3 is 60°.

Therefore,

Equation (1) would be as follows:

Tan (a-b) = Tan 30

Cancelling tan on both the sides we get:

(a-b)=30 ....(3)

Now equation (2) would be like this:

Tan (a+b) = Tan 60

Cancelling tan on both the sides we get:

(a+b) = 60 ....(4)

Solving equation (3) further we get:

a-b =30

a = 30+b

Putting the value of 'a' in equation (4):

30+b+b= 60

30+2b= 60

2b= 30

b=15.

Therefore,

a= 30+15

a= 45.

Hope it helps! :D

–TGA.