Linear Inequalities

Question
CBSEENMA11015507

In a ∆PQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then the angle R is equal to

  • 5π/6

  • π/6

  • π/4

  • 3π/4

Solution

B.

π/6

3 sin P + 4 cos Q = 6 ...... (1)
4 sin Q + 3 cos P = 1 ...... (2)
From (1) and (2) ∠P is obtuse.
(3 sin P + 4 cos Q)2+ (4 sin Q + 3 cos P)2= 37
⇒9 + 16 + 24 (sin P cos Q + cos P sin Q) = 37
⇒ 24 sin (P + Q) = 12
rightwards double arrow space sin space left parenthesis straight P space plus straight Q right parenthesis space equals space 1 half
rightwards double arrow space straight P space plus straight Q space equals space fraction numerator 5 straight pi over denominator 6 end fraction
rightwards double arrow space straight R space equals space straight pi over 6

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