By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 1 2024 Maths, question 42

Topic: Trigonometry

Q42

What is 15+cot⁡2(π4−2cot⁡−13)\sqrt{15+\cot ^{2}\left( \frac{\pi}{4}-2\cot ^{-1}3 \right)} equal to ?

  1. (a) 11
  2. (b) 77
  3. (c) 88Correct answer
  4. (d) 1616

Solution.

Answer: (c) 88

  1. Put t = cot⁻¹3, so tan t = 1/3 and tan 2t = 3/4.
  2. Then tan(π/4 − 2t) = (1 − 3/4)/(1 + 3/4) = 1/7, giving cot(π/4 − 2t) = 7.
  3. The requested square root is √(49 + 15) = 8.