Question

if tanA= 1/3 and tan B= 2 then the value of (A-B) is
A) π/2
B) π/3
C) π/4
D) π/6​

Answer 1

Step-by-step explanation:

Given

$\tan(a) = \frac{1}{3} \: and \: \tan(b) = 2$

Now,

$\tan(a - b) = \frac{ \tan(a) - \tan(b) }{1 + \tan(a) \tan(b) } \\ = \frac{ \frac{1}{3} - 2 }{1 + ( \frac{1}{3} \times 2) } \\ = \frac{ \frac{ - 5}{3} }{1 + (\frac{2}{3}) } = \frac{ \frac{ - 5}{3} }{ \frac{5}{3} } = - 1 \\ \tan((a - b) ) = - 1$

Tan(A-B)=-1=Tan(-pi/4)

So, A-B=-pi/4.

Thank you