Question

if 3tanAtanB=1 THEN Prove that cos(A-B)/cos(A+B)

Answer 1

The answer is given below :

We know that,

cos(A - B) = cosA cosB + sinA sinB
cos(A + B) = cosA cosB - sinA sinB

Given that,

3 tanA tanB = 1

or, tanA tanB = 1/3

Now,

L.H.S. = cos(A - B)/cos(A + B)

= (cosA cosB + sinA sinB)/(cosA cosB - sinA sinB)

= (1 + tanA tanB)/(1 - tanA tanB),
dividing both the numerator and denominator by (cosA cosB), since sinA/cosA = tanA

= (1 + 1/3)/(1 - 1/3)

= (4/3)/(2/3)

= 4/2

= 2

= R.H.S. [Proved]

I hope it helps you.