Question

$\tan (x+y)=a(a\ne 0)$ & $\tan (x-y)=b(b\ne 0)$ such that $\tan (x+y)+\tan (x-y)=\tan 2x$ then:

• A. $a^2+b=0$
• B. $a+b=0$
• C. $ab=0$
• D. $a-b=0$

Answer 1

The correct option is C $ab=0$

$\tan \left(2x\right)=\tan (x+g+x-y)$

$\therefore \tan 2x=\frac{a+b}{1-ab}$

$\therefore$ Given :-

$a+b=\frac{a+b}{1+ab}$

$\therefore 1-ab=1$

$\therefore ab=0$