જો alpha અને beta એ સમીકરણ sin^2,x + a, sin | vedclass

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Question

According to the given condition. $\sin \alpha+\sin \beta=-a$ and $\cos \alpha+\cos \beta=-c$

$\Rightarrow 2 \sin \frac{\alpha+\beta}{2} \cos \frac

Vedclass · Accepted Answer

$\frac{{2ac}}{{{a^2} + {c^2}}}$

Vedclass · Answer

According to the given condition. $\sin \alpha+\sin \beta=-a$ and $\cos \alpha+\cos \beta=-c$

$\Rightarrow 2 \sin \frac{\alpha+\beta}{2} \cos \frac{\alpha-\beta}{2}=-\mathrm{a}$      .....$(1)$

$	ext { and } 2 \cos \frac{\alpha+\beta}{2} \cos \frac{\alpha-\beta}{2}=-\mathrm{c}$        .....$(2)$

$(1) \div(2)$

$\Rightarrow 	an \frac{\alpha+\beta}{2}=\frac{a}{c}$

$\Rightarrow \sin (\alpha+\beta)=\frac{2 	an \frac{\alpha+\beta}{2}}{1+	an ^{2} \frac{\alpha+\beta}{2}}=\frac{2 a c}{a^{2}+c^{2}}$

Hence, $( 4)$ is the correct answer.

જો $\alpha $ અને $\beta $ એ સમીકરણ $sin^2\,x + a\, sin\, x + b = 0$ અને $cos^2\,x + c\, cos\, x + d = 0$ ના બીજો હોય તો $sin\,(\alpha + \beta )$ =

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