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

NDA 1 2024 Maths, question 41

Topic: Trigonometry

Q41

ABCABC is a triangle such that angle C=60∘C=60^{\circ}, then what is cos⁡A+cos⁡Bcos⁡(A−B2)\frac{\cos A+\cos B}{\cos \left( \frac{A-B}{2} \right)} equal to ?

  1. (a) 22
  2. (b) 2\sqrt{2}
  3. (c) 11Correct answer
  4. (d) 12\frac{1}{\sqrt{2}}

Solution.

Answer: (c) 11

  1. Using the sum-to-product identity, cos A + cos B = 2 cos((A + B)/2) cos((A − B)/2).
  2. Since A + B = 120°, the factor 2 cos 60° is 1.
  3. The requested ratio is therefore 1.