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Question

$I n a triangle A B C comma a left parenthesis c o s squared invisible function application B plus c o s squared invisible function application C right parenthesis plus c o s invisible function application A left parenthesis c c o s invisible function application C plus b c o s invisible function application B right parenthesis equals$

a
b
c
$a + b + c$

hint Hint:

First we will rearrange the terms then we will use the trigonometric formula $a equals space b cos open parentheses C close parentheses plus c cos open parentheses B close parentheses b space equals space c cos open parentheses A close parentheses plus a cos open parentheses C close parentheses c equals space a cos open parentheses B close parentheses plus b cos open parentheses A close parentheses$ .

The correct answer is: $a plus b plus c$

Step1: Rewriting the expression
$a cos squared open parentheses B close parentheses plus a cos squared open parentheses C close parentheses plus space c cos open parentheses A close parentheses cos open parentheses C close parentheses plus b cos open parentheses A close parentheses cos open parentheses B close parentheses$
=> $a cos squared open parentheses B close parentheses plus b cos open parentheses A close parentheses cos open parentheses B close parentheses plus a cos squared open parentheses C close parentheses plus space c cos open parentheses A close parentheses cos open parentheses C close parentheses$
Step2: Using the trigonometric formula
$a equals space b cos open parentheses C close parentheses plus c cos open parentheses B close parentheses b space equals space c cos open parentheses A close parentheses plus a cos open parentheses C close parentheses c equals space a cos open parentheses B close parentheses plus b cos open parentheses A close parentheses$
=> $cos open parentheses B close parentheses left parenthesis a cos open parentheses B close parentheses plus b cos open parentheses A close parentheses right parenthesis plus cos open parentheses C close parentheses left parenthesis a cos open parentheses C close parentheses plus space c cos open parentheses A close parentheses right parenthesis$
=> $c cos open parentheses B close parentheses plus b cos open parentheses C close parentheses$
Step3: Again using the trigonometric formula
=> $c cos open parentheses B close parentheses plus b cos open parentheses C close parentheses$
=> $a$

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