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Question

In $capital delta A B C comma c left parenthesis a cos invisible function application B minus b cos invisible function application A right parenthesis equals$

$a^{2} - b^{2}$
$a^{2} + b^{2}$
$b^{2} - c^{2}$
$b^{2} + c^{2}$

hint Hint:

In this question we have to use cosine rule $cos open parentheses B close parentheses equals space fraction numerator a squared plus c squared minus b squared over denominator 2 a c end fraction cos open parentheses A close parentheses equals fraction numerator b squared plus c squared minus a squared over denominator 2 b c end fraction$

The correct answer is: $a squared minus b squared$

In this question we have to find the value of $c left parenthesis a cos open parentheses B close parentheses minus b cos open parentheses A close parentheses right parenthesis$
Step1: Using Cosine Rule
$cos open parentheses B close parentheses equals space fraction numerator a squared plus c squared minus b squared over denominator 2 a c end fraction cos open parentheses A close parentheses equals fraction numerator b squared plus c squared minus a squared over denominator 2 b c end fraction$
=> $c left parenthesis a cross times fraction numerator a squared plus c squared minus b squared over denominator 2 a c end fraction minus b cross times fraction numerator b squared plus c squared minus a squared over denominator 2 b c end fraction right parenthesis$
=> $fraction numerator a squared plus c squared minus b squared over denominator 2 end fraction minus left parenthesis fraction numerator b squared plus c squared minus a squared over denominator 2 end fraction right parenthesis$
=> $fraction numerator a squared plus c squared minus b squared minus b squared minus c squared plus a squared over denominator 2 end fraction$
=> $a squared minus b squared$

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