Question

Assertion :$\frac{\tan 3x-\tan 2x}{1+\tan 2x\tan 3x}=1$, then $x=n\pi +\frac{\pi }{4},\forall n\in I$ Reason: $\tan x$ is not defined at $x=n\pi +\frac{\pi }{2},n\in I$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
• C. Assertion is correct but Reason is incorrect.
• D. Assertion false but Reason is true.

Answer 1

The correct option is D Assertion false but Reason is true.

$\tan (A-B)=\frac{\tan A-\tan B}{1+\tan A.\tan B}$
Applying this we get
$\tan x=1$ or $x=\frac{\pi }{4}$
However
$\tan 2x=\tan \frac{\pi }{2}=\infty$ or not defined.
Hence there is no solution.
Thus $\tan x$ is not defined at $x=\frac{(2n+1)\pi }{2}$ where $nϵN$.