In a triangle ABC,if frac{a}{b^2-c^2} + frac{ | vedclass

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

Question

(D) Given,$\frac{a}{b^2-c^2} + \frac{c}{b^2-a^2} = 0$.Using the sine rule $a = 2R \sin A$,$b = 2R \sin B$,$c = 2R \sin C$:$\frac{2R \sin A}{4R^2(\sin^

Vedclass · Accepted Answer

$\frac{\pi}{3}$

Vedclass · Answer

(D) Given,$\frac{a}{b^2-c^2} + \frac{c}{b^2-a^2} = 0$.Using the sine rule $a = 2R \sin A$,$b = 2R \sin B$,$c = 2R \sin C$:$\frac{2R \sin A}{4R^2(\sin^2 B - \sin^2 C)} + \frac{2R \sin C}{4R^2(\sin^2 B - \sin^2 A)} = 0$$\frac{\sin A}{\sin(B+C)\sin(B-C)} + \frac{\sin C}{\sin(B+A)\sin(B-A)} = 0$Since $A+B+C = \pi$,$\sin(B+C) = \sin A$ and $\sin(B+A) = \sin C$:$\frac{\sin A}{\sin A \sin(B-C)} + \frac{\sin C}{\sin C \sin(B-A)} = 0$$\frac{1}{\sin(B-C)} + \frac{1}{\sin(B-A)} = 0$$\sin(B-A) = -\sin(B-C) = \sin(C-B)$$B-A = C-B$ or $B-A = \pi - (C-B)$$2B = A+C$. Since $A+B+C = \pi$,$A+C = \pi - B$.$2B = \pi - B$ $\Rightarrow 3B = \pi$ $\Rightarrow B = \frac{\pi}{3}$.

List-$I$	List-$II$
$(A)$ $[\mathbf{a} \mathbf{b} \mathbf{c}]$	$1. \|\mathbf{a}\|\|\mathbf{b}\|\cos(\mathbf{a}, \mathbf{b})$
$(B)$ $(\mathbf{c} \times \mathbf{a}) \times \mathbf{b}$	$2. (\mathbf{a} \cdot \mathbf{c})\mathbf{b} - (\mathbf{a} \cdot \mathbf{b})\mathbf{c}$
$(C)$ $\mathbf{a} \times (\mathbf{b} \times \mathbf{c})$	$3. \mathbf{a} \cdot \mathbf{b} \times \mathbf{c}$
$(D)$ $\mathbf{a} \cdot \mathbf{b}$	$4. \|\mathbf{a}\|\|\mathbf{b}\|$
	$5. (\mathbf{b} \cdot \mathbf{c})\mathbf{a} - (\mathbf{a} \cdot \mathbf{b})\mathbf{c}$

In a $\triangle ABC$,if $\frac{a}{b^2-c^2} + \frac{c}{b^2-a^2} = 0$,then $B$ is equal to

Similar Questions

Which of the following are found in extreme saline conditions?

Dividing the interval $[0,6]$ into $6$ equal parts and by using the trapezoidal rule, the value of $\int_0^6 x^3 dx$ is approximately:

Which of the following is a characteristic of $Pteridophytes$?

If $a$ stands for the edge length of the cubic systems: simple cubic,body-centered cubic,and face-centered cubic,then the ratio of radii of the spheres in these systems will be respectively:

Vedclass Test Series

Exam Paper Generator

Online Exam Module