Question

if tanA = 3 and tanB = 1/2 prove that A - B = π/4​

Answer 1

Given →

tan A = 3 and tan B = 1/2

Solution →

tan ( A- B ) = $\frac{tanA - tanB }{1 + tan A. tan B}$

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

$= > \tan(a - b) = \frac{ \frac{5}{2} }{ \frac{5}{2} }$

=> tan ( A - B) = 1

=> tan ( A - B) = tan 45°

Degree to radian conversion →

$= > \frac{45 \times \pi}{180}$

$= > \tan(45) = \tan \frac{\pi}{4}$

→ tan (A - B) = tan π/4

→ A - B = π/4

Answer 2

Given

tanA = 3

tanB = 1/2

Formula

$\tan(a - b) = \frac{ \tan(a) - \tan(b) }{1 + \tan(a) \tan(b) }$

a - b = π/4

using tan

tan(a - b) = 1

Now

LHS

$\tan(a - b) \\ \frac{ \tan(a) - \tan(b) }{1 + \tan( \alpha ) \tan( b) }$

on putting the value

$\frac{3 - \frac{1}{2} }{1 + \frac{3}{2} } \\ \frac{ \frac{5}{2} }{ \frac{5}{2} } \\ 1 \\ so \\ lhs = rhs \:$