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Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions1 Mark
Question
In $\triangle ABC$, prove that $( a + b ) \cos C +( b + c ) \cos A +( c + a ) \cos B = a + b + c$
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Answer

$\begin{aligned} \text { L.H.S. } & =(a+b) \cos C+(b+c) \cos A+(c+a) \cos B \\ & =(a \cos C+b \cos C)+(b \cos A+c \cos A)+(c \cos B+a \cos B) \\ & =(a \cos C+c \cos A)+(b \cos A+a \cos B)+(c \cos B+b \cos C) \\ & =a+b+c=\text { R.H.S. }\end{aligned}$

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