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Maths-

General

Easy

Question

If $b divided by left parenthesis c plus a right parenthesis plus c divided by left parenthesis a plus b right parenthesis equals 1 space$ then

$A = 60^{\circ}$
$B = 60^{\circ}$
$C = 60^{\circ}$
$A = 90^{\circ}$

hint Hint:

In this question we have to use Cosine Rule
$cos open parentheses A close parentheses equals space fraction numerator b squared plus c squared minus a squared over denominator 2 b c end fraction$
=> $b squared plus c squared equals 2 b c cos open parentheses A close parentheses plus a squared$

The correct answer is: $A equals 60 to the power of ring operator$

In this question we are given $fraction numerator b over denominator a plus c end fraction plus fraction numerator c over denominator a plus b end fraction equals 1$
By Taking LCM and then adding we get,
$fraction numerator b left parenthesis a plus b right parenthesis plus c left parenthesis a plus c right parenthesis over denominator left parenthesis a plus c right parenthesis left parenthesis a plus b right parenthesis end fraction equals 1$
=> $fraction numerator b squared plus c squared plus a b plus a c over denominator left parenthesis a squared plus a b plus a c plus b c right parenthesis end fraction equals 1$

By using Cosine Rule
$cos open parentheses A close parentheses equals space fraction numerator b squared plus c squared minus a squared over denominator 2 b c end fraction$
=> $b squared plus c squared equals 2 b c cos open parentheses A close parentheses plus a squared$
=> $2 b c cos open parentheses A close parentheses plus a squared plus a b plus a c equals a squared plus a b plus a c plus b c$
=> $2 b c cos open parentheses A close parentheses equals b c$
=> $cos open parentheses A close parentheses equals 1 half$
$A equals 60 degree$

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