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Question

left parenthesis I n space triangle A B C comma left parenthesis cos invisible function application C plus cos invisible function application A right parenthesis divided by left parenthesis c plus a right parenthesis plus left parenthesis cos invisible function application B right parenthesis divided by b equals & right parenthesis

  1. 1 divided by a
  2. 1 divided by b
  3. 1 divided by straight c
  4. left parenthesis c plus a right parenthesis divided by b

hintHint:

First we will take the LCM and then use these formulas to get the final answer. a space equals space b cos open parentheses C close parentheses plus c cos open parentheses B close parentheses
b equals 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: 1 divided by straight c


    In this question we have to find the value of the expression.
    fraction numerator cos open parentheses C close parentheses plus cos open parentheses A close parentheses over denominator a plus c end fraction plus fraction numerator cos open parentheses B close parentheses over denominator b end fraction
    Step1:  Taking LCM
    =>fraction numerator b cos open parentheses C close parentheses plus b cos open parentheses A close parentheses plus a cos open parentheses B close parentheses plus c cos open parentheses B close parentheses over denominator b left parenthesis a plus c right parenthesis end fraction
    Step2: By using the trigonometric formula
    a space equals space b cos open parentheses C close parentheses plus c cos open parentheses B close parentheses
b equals 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
    =>fraction numerator a plus c over denominator b left parenthesis a plus c right parenthesis end fraction
    =>1 over b
    So, the value of the expression is 1 over b.

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