Question

IF TAN(A+B) =√3,TAN(A-B)=1/√3,FIND A AND B.ALSO CALCULATE TANA tan(A+B) + COSA TAN(A-B)

Answer 1

Answer:

Step-by-step explanation:

Here its given that Tan (A+B) = root 3...(1)

And tan(A-B)=1/root 3...................(2)

We know that Tan 60 is root 3..........(3)

And that Tan 30 is 1/root 3..........(4)

From 1 and 3

A+B = 60

And from 2 and 4

A-B = 30

So, Solving the equations we get

A=45 and B=15

Now Tan A (Tan (A-B)) + Cos A(Tan (A-B))

Tan 45 =1

And cos 45 = 1/root 2

So solving the equation we get

1(root 3) + 1/root 2(1/root 3)

root 3 + 1/root 6

root 3 + root 6/6...........(on rationalizing)

Taking LCM and adding we get

(6 root3 + root6)/6

This is the final answer

Hope it helps...

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