Maths-
General
Easy

Question

If cos theta equals 3 over 5 and theta is not in the first quadrant, then fraction numerator 5 tan space left parenthesis pi plus theta right parenthesis plus 4 cos space left parenthesis pi plus theta right parenthesis over denominator secc space left parenthesis 2 pi minus theta right parenthesis minus 4 cot space left parenthesis 2 pi plus theta right parenthesis end fraction equals

  1. 4 over 5
  2. negative 4 over 5
  3. 5 over 4
  4. negative 5 over 4

hintHint:

cos x is positive in 1st and 4th quadrant only. So, since theta is not in the first quadrant, it lies in the fourth quadrant.

The correct answer is: negative 4 over 5


    Step by step solution:
    cos theta space equals space 3 over 5
    theta lies in the fourth quadrant.
    rightwards double arrow tan A space equals space minus 4 over 3
    rightwards double arrow s e c theta equals 5 over 3
    rightwards double arrow c o t theta equals negative 3 over 4
    now,
    fraction numerator 5 tan space left parenthesis pi plus theta right parenthesis plus 4 cos space left parenthesis pi plus theta right parenthesis over denominator secc space left parenthesis 2 pi minus theta right parenthesis minus 4 cot space left parenthesis 2 pi plus theta right parenthesis end fraction equalsfraction numerator 5 left parenthesis negative tan theta right parenthesis plus 4 left parenthesis negative cos theta right parenthesis over denominator s e c theta minus 4 left parenthesis negative c o t theta right parenthesis end fractionequals fraction numerator negative 5 tan theta minus 4 cos theta over denominator s e c theta plus 4 c o t theta end fraction=fraction numerator negative 5 open parentheses negative begin display style 4 over 3 end style close parentheses minus 4 open parentheses begin display style 3 over 5 end style close parentheses over denominator begin display style 5 over 3 end style plus 4 open parentheses negative begin display style 3 over 4 end style close parentheses end fractionequals fraction numerator begin display style 20 over 3 end style minus begin display style 12 over 5 end style over denominator begin display style 5 over 3 end style minus 3 end fractionequals fraction numerator begin display style fraction numerator 100 minus 36 over denominator 15 end fraction end style over denominator begin display style fraction numerator 5 minus 9 over denominator 3 end fraction end style end fractionequals fraction numerator begin display style 64 over 15 end style over denominator negative begin display style 16 over 3 end style end fractionequals negative 4 over 5
    Hence, option(b) is the correct option.

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