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

NDA 1 2024 Maths, question 37

Topic: Trigonometry

Q37

What is (sin⁡9∘−cos⁡9∘)(\sin 9^{\circ}-\cos 9^{\circ}) equal to ?

  1. (a) −5−52-\frac{\sqrt{5-\sqrt{5}}}{2}Correct answer
  2. (b) −5−32-\frac{\sqrt{5-\sqrt{3}}}{2}
  3. (c) 5−52\frac{\sqrt{5-\sqrt{5}}}{2}
  4. (d) 5−54\frac{\sqrt{5-\sqrt{5}}}{4}

Solution.

Answer: (a) −5−52-\frac{\sqrt{5-\sqrt{5}}}{2}

  1. Since 9° < 45°, sin 9° − cos 9° is negative.
  2. Its square is 1 − sin 18° = (5 − √5)/4.
  3. Taking the negative square root gives −½√(5 − √5).