If tan A and tan B are the roots of the quadr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given that $	an A$ and $	an B$ are the roots of the quadratic equation $x^2-px+q=0$. By the relation between roots and coefficients,we have: $

Vedclass · Accepted Answer

$\frac{p^2}{p^2+(1-q)^2}$

Vedclass · Answer

(D) Given that $	an A$ and $	an B$ are the roots of the quadratic equation $x^2-px+q=0$. By the relation between roots and coefficients,we have: $	an A + 	an B = p$ $	an A 	an B = q$ Using the trigonometric identity for $	an(A+B)$: $	an(A+B) = \frac{	an A + 	an B}{1 - 	an A 	an B} = \frac{p}{1-q}$ Now,we know that $\sin^2 	heta = \frac{	an^2 	heta}{1 + 	an^2 	heta}$. Substituting $	an(A+B) = \frac{p}{1-q}$: $\sin^2(A+B) = \frac{(\frac{p}{1-q})^2}{1 + (\frac{p}{1-q})^2} = \frac{\frac{p^2}{(1-q)^2}}{\frac{(1-q)^2 + p^2}{(1-q)^2}} = \frac{p^2}{p^2+(1-q)^2}$

If $\tan A$ and $\tan B$ are the roots of the quadratic equation $x^2-px+q=0$,then $\sin^2(A+B)$ is equal to

Similar Questions

If $x \neq -y$ and $\sin x + \sin y = 3(\cos y - \cos x)$,then $\tan(x - y) =$

If $\sin(\theta) + \operatorname{cosec}(\theta) = 2$,then $\sin^{2020}(\theta) + \operatorname{cosec}^{2020}(\theta) = \dots$

$(\sec A + \tan A - 1)(\sec A - \tan A + 1) - 2\tan A = $

$\sin ^3 10^{\circ}+\sin ^3 50^{\circ}-\sin ^3 70^{\circ}=$

$\sin 12^\circ \sin 24^\circ \sin 48^\circ \sin 84^\circ = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module