Question

Assertion :If tan A, tan B are the roots of equation $x^2-px-1=0$, then
${\sin }^2(A+B)=\frac{p^2}{1+p^2}$ Reason: ${\sin }^2(A+B)=\frac{ta{n}^2(A+B)}{1+ta{n}^2(A+B)}$

• 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 D Assertion is incorrect but Reason is correct

From the question, we can write

$\tan A+\tan B=p$
And $\tan A.\tan B=-1$
Hence, $\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A.\tan B}$

$=\frac{p}{2}$.
Hence, $\sin (A+B)=\frac{p}{\sqrt{2^2+p^2}}$
${\sin }^2(A+B)=\frac{p^2}{4+p^2}$.