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Question

In $triangle A B C comma 4 R s sin invisible function application A divided by 2 space sin invisible function application B divided by 2 space sin invisible function application C divided by 2 equals$

$Δ$
2 $Δ$
r
2r

hint Hint:

In this question we have to use the formula of Solution of triangle.
$sin open parentheses A over 2 close parentheses equals square root of fraction numerator left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator b c end fraction end root sin open parentheses B over 2 close parentheses equals square root of fraction numerator left parenthesis s minus c right parenthesis left parenthesis s minus a right parenthesis over denominator a c end fraction end root sin open parentheses C over 2 close parentheses equals square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis over denominator a b end fraction end root$
and $S squared equals space s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis$ , $fraction numerator a b c over denominator 4 R end fraction equals S$ and $S over s equals r$

The correct answer is: $capital delta$

In this question we have to find the value of $4 R sin open parentheses A over 2 close parentheses sin open parentheses B over 2 close parentheses sin open parentheses C over 2 close parentheses$
We know that $sin open parentheses A over 2 close parentheses equals square root of fraction numerator left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator b c end fraction end root space sin open parentheses B over 2 close parentheses equals square root of fraction numerator left parenthesis s minus c right parenthesis left parenthesis s minus a right parenthesis over denominator a c end fraction end root sin open parentheses C over 2 close parentheses equals square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis over denominator a b end fraction end root$
By putting these values in the given expression
=> $4 R square root of fraction numerator left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator b c end fraction end root cross times square root of fraction numerator left parenthesis s minus c right parenthesis left parenthesis s minus a right parenthesis over denominator a c end fraction end root cross times square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis over denominator a b end fraction end root$
=> $4 R square root of fraction numerator left parenthesis s minus a right parenthesis squared left parenthesis s minus b right parenthesis squared left parenthesis s minus c right parenthesis squared over denominator a squared b squared c squared end fraction end root$
=> $4 R fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator a b c end fraction$
We know that $S squared equals space s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis$ , $fraction numerator a b c over denominator 4 R end fraction equals S$ and $S over s equals r$
=> $1 over S cross times S squared over s$
=> $S over s$
=> $r$

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parallel

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parallel

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parallel

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,

If $f left parenthesis a right parenthesis equals 2 comma f to the power of apostrophe left parenthesis a right parenthesis equals 1 comma g left parenthesis a right parenthesis equals negative 1 comma g to the power of factorial left parenthesis a right parenthesis equals 2 comma$ then the value of $L i m subscript left parenthesis x rightwards arrow a right parenthesis invisible function application left parenthesis g left parenthesis x right parenthesis f left parenthesis a right parenthesis minus g left parenthesis a right parenthesis f left parenthesis x right parenthesis right parenthesis divided by left parenthesis x minus a right parenthesis$ is
,

parallel

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