Question

If A = 60°, B = 30° verify that tan( A - B) = ${\displaystyle \frac{\tan A-\tan B}{1+\tan A.\tan B}}$.

Answer 1

It is given that A = 60°, B = 30° 
Putting A = 60° and B = 30° in the given equation,
we get

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

⇒ tan( 60° - 30° ) = ${\displaystyle \frac{\tan 60°-\tan 30°}{1+\tan 60°.\tan 30°}}$

⇒ tan 30° = ${\displaystyle \frac{\sqrt{3}-\frac{1}{\sqrt{3}}}{1+\sqrt{3}\times \frac{1}{\sqrt{3}}}}$

⇒ ${\displaystyle \frac{\frac{3-1}{\sqrt{3}}}{2}}$

⇒ ${\displaystyle \frac{\frac{2}{\sqrt{3}}}{\frac{2}{1}}}$

⇒ ${\displaystyle \frac{2}{2\sqrt{3}}}$

⇒ ${\displaystyle \frac{1}{\sqrt{3}}}$

⇒ LHS = RHS