CDS 2026 (I) Elementary Mathematics, question 97

Topic: Trigonometry

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Passage · Q97 to Q98

p+qcot⁡θ=3cosec⁡θp+q\cot \theta=3\operatorname{cosec} \theta and

q−pcot⁡θ=2cosec⁡θq-p\cot \theta=2\operatorname{cosec} \theta

Q97

What is p2+q2p^{2}+q^{2} equal to ?

  1. (a) 55
  2. (b) 77
  3. (c) 1010
  4. (d) 1313Correct answer

Solution.

Answer: (d) 1313

  1. Multiply both shared equations by sin⁡θ\sin\theta to obtain psin⁡θ+qcos⁡θ=3p\sin\theta + q\cos\theta = 3 and qsin⁡θ−pcos⁡θ=2q\sin\theta - p\cos\theta = 2.
  2. Squaring and adding cancels the cross terms: (p2+q2)(sin⁡2θ+cos⁡2θ)=9+4\left( p^{2} + q^{2} \right)\left( \sin^{2}\theta + \cos^{2}\theta \right) = 9 + 4.