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    Maths-
    General
    Easy

    Question

    in a triangle P Q R 3 sin space P plus 4 cos space Q equals 6 and 4 sin space Q plus 3 cos p=1 then

    1. pi over 4
    2. fraction numerator 3 pi over denominator 4 end fraction
    3. fraction numerator 5 pi over denominator 6 end fraction
    4. pi over 6

    hintHint:

    In the question it is given that, in  triangle P Q R,  3 sin space P plus 4 cos space Q equals 6 and 4 sin space Q plus 3 cos space Pequals 1. We are required to find angle R.

    The correct answer is: pi over 6

      Step by step solution:
      Given,
      3 sin P plus 4 cos Q to the power of blank equals 6     -(i)
      4 sin Q plus 3 cos P equals 1      -(ii)
      On squaring and adding both the equations, we get,
      open parentheses 3 space sin space P space plus space 4 space cos space Q close parentheses squaredplus space left parenthesis 4 space sin space Q space plus space 3 space cos space P right parenthesis squaredequals 36 plus 1
      rightwards double arrow 9 space sin squared P space plus space 16 space cos squared Q spaceplus space 24 sin space P space cos space Q spaceplus space 16 space sin squared Q space plusspace 9 space cos squared P space plusspace 24 space sin space Q space cos space P space equals 37
      rightwards double arrow 9 space plus space 16 spaceplus 24 left parenthesis sin P space cos Q spaceplus space sin Q cos P right parenthesis space equals space 37                      [ since  sin squared theta space plus space cos squared theta equals 1 ]
      rightwards double arrow 24 space sin left parenthesis space P plusQ right parenthesis space equals space 37 space minus space 25
      rightwards double arrow sin space left parenthesis P plus Q right parenthesis space equals 12 over 24equals 1 half
      rightwards double arrow sin left parenthesis P plus Q right parenthesis space equals spacesin space 30 degree space o r space sin space 150 degree
      rightwards double arrow space P plus Q space equals space30 degree space o r space 150 degree
      Since, PQR is a triangle, therefore, angle P plus angle Q plus angle R space equals space 180 degree
      angle R equals space 150 degree
      rightwards double arrow angle R space equals space fraction numerator 3 straight pi over denominator 4 end fraction
      Hence, option(c) is the correct option.

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