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Sine And Cosine Formulae And Their Applications — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSSine And Cosine Formulae And Their Applications2 Marks
Question
$\text{a}(\sin\text{B}-\sin\text{C})+\text{b}(\sin\text{C}-\sin\text{A})+\text{c}(\sin\text{A}-\sin\text{B})=0$
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Answer

$\text{a}(\sin\text{B}-\sin\text{C})+\text{b}(\sin\text{C}-\sin\text{A})+\text{c}(\sin\text{A}-\sin\text{B})=0$
$\text{LHS}=\text{a}(\sin\text{B}-\sin\text{C})+\text{b}(\sin\text{C}-\sin\text{A})+\text{c}(\sin\text{A}-\sin\text{B})$
$=\text{a}\sin\text{B}-\text{a}\sin\text{C}+\text{b}\sin\text{C}-\text{b}\sin\text{A}+\text{c}\sin\text{A}-\text{c}\sin\text{B}$
$=\text{b}\sin\text{A}-\text{c}\sin\text{A + c}\sin\text{B}-\text{b}\sin\text{A + c}\sin\text{A}-\text{c}\sin\text{B}$ $[\because \text{b}\sin\text{A = a}\sin\text{B,b}\sin\text{C = c}\sin]$
$=0=\text{RHS}$
Hence Proved

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