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

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSine and Cosine Formulae and Their Applications1 Mark
Question
In any $\triangle\text{ABC},$ find the value of $\sum\text{a}(\sin\text{B}-\sin\text{C})$
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Answer

let $\text{a}\sin\text{B = b}\sin\text{A,b}\sin\text{C = c}\sin\text{A,a}\sin\text{C = c}\sin\text{A}$ $\sum\text{a}(\sin\text{B}-\sin\text{C})$ $=\text{a}(\sin\text{B}-\sin\text{C})+\text{b}(\sin\text{C}-\sin\text{A})+\text{c}(\sin\text{A}-\sin\text{B})$ $=\text{a}\sin\text{B}-\text{a}\sin\text{C + b}\sin\text{C}-\text{b}\sin\text{A + c}\sin\text{A}-\text{c}\sin\text{B}$ $=\text{b}\sin\text{A}-\text{a}\sin\text{C + b}\sin\text{C}-\text{b}\sin\text{A + a}\sin\text{C}-\text{b}\sin\text{C}$ $=0$

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