Question

Assertion :In a triangle ABC if $tanA:tanB:tanC=1:2:3$ then $A={45}^o$ Reason: If$p:q:r=1:2:3$ then $p=1$

• 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 is incorrect but Reason is correct

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

Let $\tan A=k$
$\tan B=2k$
$\tan C=3k$
Now
$\tan A+\tan B+\tan C=\tan A.\tan B.\tan C$
$k=k^3$
$k(k^2-1)=0$
$k=0$ and $k=\pm 1$
Now , $k=0$ is not possible and there can be maximum of one obtuse angle.
Hence $k=-1$ is also not possible.
Hence
$k=1$.
Therefore $\tan A=k=1$
$\therefore A={45}^0$.