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Maths-

General

Easy

Question

If $A equals 60 to the power of ring operator$ then the value of $left parenthesis 1 plus a divided by c plus b divided by c right parenthesis left parenthesis 1 plus c divided by b minus a divided by b right parenthesis equals$

3
2
1
$2 a b c$

hint Hint:

In this question we will use the cosine rule $cos open parentheses A close parentheses space equals space fraction numerator b squared plus c squared minus a squared over denominator 2 b c end fraction$ where $angle A equals 60 degree$

The correct answer is: 3

In this question we have to find the value of $open parentheses 1 plus a over c plus b over c close parentheses open parentheses 1 plus c over b minus a over b close parentheses$
=> $open parentheses fraction numerator b plus c plus a over denominator c end fraction close parentheses open parentheses fraction numerator b plus c minus a over denominator b end fraction close parentheses$
By using the formula of $left parenthesis a plus b right parenthesis left parenthesis a minus b right parenthesis equals space a squared minus b squared$
=> $fraction numerator left parenthesis b plus c right parenthesis squared minus a to the power of 2 end exponent over denominator b c end fraction$
=> $fraction numerator b squared plus c squared plus 2 b c minus a squared over denominator b c end fraction$
=> $fraction numerator b squared plus c squared minus a squared over denominator b c end fraction plus fraction numerator 2 b c over denominator b c end fraction$
By using cosine rule $cos open parentheses A close parentheses space equals space fraction numerator b squared plus c squared minus a squared over denominator 2 b c end fraction$ where $angle A equals 60 degree$
=> $cos open parentheses 60 degree close parentheses equals 1 half$
=> $1 half equals space fraction numerator b squared plus c squared minus a squared over denominator 2 b c end fraction$
=> $b squared plus c squared minus a squared space equals space b c$
=> $fraction numerator b c over denominator b c end fraction plus fraction numerator 2 b c over denominator b c end fraction$
=> $3$
Hence, the value of the expression is $3$

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