If frac{tan (alpha+beta-gamma)}{tan (alpha-be | vedclass

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

Question

(A) Given $\frac{	an (\alpha+\beta-\gamma)}{	an (\alpha-\beta+\gamma)}=\frac{	an \gamma}{	an \beta}$.Applying componendo and dividendo:$\frac{	an

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) Given $\frac{	an (\alpha+\beta-\gamma)}{	an (\alpha-\beta+\gamma)}=\frac{	an \gamma}{	an \beta}$.Applying componendo and dividendo:$\frac{	an (\alpha+\beta-\gamma)+	an (\alpha-\beta+\gamma)}{	an (\alpha+\beta-\gamma)-	an (\alpha-\beta+\gamma)}=\frac{	an \gamma+	an \beta}{	an \gamma-	an \beta}$.Using $	an A + 	an B = \frac{\sin(A+B)}{\cos A \cos B}$ and $	an A - 	an B = \frac{\sin(A-B)}{\cos A \cos B}$,we get:$\frac{\sin(2\alpha)}{\sin(2\beta-2\gamma)} = \frac{\sin(\gamma+\beta)}{\sin(\gamma-\beta)}$.$\sin(2\alpha) = \frac{\sin(\gamma+\beta) \sin(2\beta-2\gamma)}{\sin(\gamma-\beta)} = \frac{\sin(\gamma+\beta) \cdot 2 \sin(\beta-\gamma) \cos(\beta-\gamma)}{-(\sin(\beta-\gamma))} = -2 \sin(\beta+\gamma) \cos(\beta-\gamma)$.Using $2 \sin A \cos B = \sin(A+B) + \sin(A-B)$:$\sin(2\alpha) = -(\sin(2\beta) + \sin(2\gamma))$.Therefore,$\sin 2\alpha + \sin 2\beta + \sin 2\gamma = 0$.

If $\frac{\tan (\alpha+\beta-\gamma)}{\tan (\alpha-\beta+\gamma)}=\frac{\tan \gamma}{\tan \beta}$ and $\beta \neq \gamma$,then the value of $\sin 2 \alpha+\sin 2 \beta+\sin 2 \gamma$ is

Similar Questions

$\cos ^2 5^{\circ}-\cos ^2 15^{\circ}-\sin ^2 15^{\circ}+\sin ^2 35^{\circ}+\cos 15^{\circ} \sin 15^{\circ}-\cos 5^{\circ} \sin 35^{\circ} = $

Let $A_0 A_1 A_2 A_3 A_4 A_5$ be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments $A_0 A_1$,$A_0 A_2$,and $A_0 A_4$ is

If $\tan A - \tan B = x$ and $\cot A - \cot B = y$,then $\cot (A - B) =$

The extreme values of $4 \cos \left(x^2\right) \cos \left(\frac{\pi}{3}+x^2\right) \cos \left(\frac{\pi}{3}-x^2\right)$ over $\mathbb{R}$ are

If $0 < \theta < \frac{\pi}{2}$ and $\sin \theta \cos \theta = \frac{12}{25}$,then $\sin^4 \theta + \cos^4 \theta$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module