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NDA 2 2024 Maths, question 32

Topic: Trigonometry

Q32

If

xcos⁡θ=ycos⁡(2π3−θ)=zcos⁡(2π3+θ)\frac{x}{\cos \theta}=\frac{y}{\cos \left( \frac{2\pi}{3}-\theta \right)}=\frac{z}{\cos \left( \frac{2\pi}{3}+\theta \right)}

then what is x+y+zx+y+z equal to?

  1. (a) −1-1
  2. (b) 00Correct answer
  3. (c) 11
  4. (d) 33

Solution.

Answer: (b) 00

  1. Let the common ratio be t.
  2. Then x+y+z=t[cosθ+cos(2π/3−θ)+cos(2π/3+θ)].
  3. The last two cosines sum to 2cos(2π/3)cosθ=−cosθ, making the bracket zero.