If b sin alpha = a sin (alpha + 2beta),then f | vedclass

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

Question

(C) Given $b \sin \alpha = a \sin (\alpha + 2\beta)$.$\frac{a}{b} = \frac{\sin \alpha}{\sin (\alpha + 2\beta)}$.Using componendo and dividendo,we get:

Vedclass · Accepted Answer

$\frac{-\cot \beta}{\cot (\alpha + \beta)}$

Vedclass · Answer

(C) Given $b \sin \alpha = a \sin (\alpha + 2\beta)$.$\frac{a}{b} = \frac{\sin \alpha}{\sin (\alpha + 2\beta)}$.Using componendo and dividendo,we get:$\frac{a + b}{a - b} = \frac{\sin \alpha + \sin (\alpha + 2\beta)}{\sin \alpha - \sin (\alpha + 2\beta)}$.Applying the sum-to-product formulas $\sin C + \sin D = 2 \sin \frac{C+D}{2} \cos \frac{C-D}{2}$ and $\sin C - \sin D = 2 \cos \frac{C+D}{2} \sin \frac{C-D}{2}$:Numerator: $\sin \alpha + \sin (\alpha + 2\beta) = 2 \sin(\alpha + \beta) \cos(-\beta) = 2 \sin(\alpha + \beta) \cos \beta$.Denominator: $\sin \alpha - \sin (\alpha + 2\beta) = 2 \cos(\alpha + \beta) \sin(-\beta) = -2 \cos(\alpha + \beta) \sin \beta$.Therefore,$\frac{a + b}{a - b} = \frac{2 \sin(\alpha + \beta) \cos \beta}{-2 \cos(\alpha + \beta) \sin \beta} = -	an(\alpha + \beta) \cot \beta$.This can be rewritten as $-\frac{\cot \beta}{\cot(\alpha + \beta)}$.

If $b \sin \alpha = a \sin (\alpha + 2\beta)$,then $\frac{a + b}{a - b} = $

Similar Questions

If $\frac{3\pi}{4} < \alpha < \pi,$ then $\sqrt{\csc^2 \alpha + 2\cot \alpha}$ is equal to

$\log \sin 1^{\circ} \cdot \log \sin 2^{\circ} \cdot \log \sin 3^{\circ} \cdot \ldots \cdot \log \sin 179^{\circ} = ?$

The value of $\sec ^{2} \theta - \frac{\sin ^{2} \theta - 2 \sin ^{4} \theta}{2 \cos ^{4} \theta - \cos ^{2} \theta}$ is

The value of the following expression is $3(\sin^{4} \theta + \cos^{4} \theta) + 2(\sin^{6} \theta + \cos^{6} \theta) + 12\sin^{2} \theta \cos^{2} \theta$.

Let $f(x) = \max (\sin x, \cos x)$ and $g(x) = \min (\cos x, \sin x)$. If the equation $f(x)y^2 + ay + g(x) = 0$ has real roots for all $x \in R$,then the complete set of values of $a$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module