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NDA 1 2024 Maths, question 43

Topic: Trigonometry

Q43

What is the value of sin⁡10∘⋅sin⁡50∘+sin⁡50∘⋅sin⁡250∘+sin⁡250∘⋅sin⁡10∘\sin 10^{\circ}\cdot \sin 50^{\circ}+\sin 50^{\circ}\cdot \sin 250^{\circ}+\sin 250^{\circ}\cdot \sin 10^{\circ} equal to ?

  1. (a) −14-\frac{1}{4}
  2. (b) −34-\frac{3}{4}Correct answer
  3. (c) 3sin⁡10∘4\frac{3\sin 10^{\circ}}{4}
  4. (d) −3cos⁡10∘4-\frac{3\cos 10^{\circ}}{4}

Solution.

Answer: (b) −34-\frac{3}{4}

  1. Write sin 50° as sin 130°.
  2. The sines at 10°, 130° and 250° sum to zero and their squared values sum to 3/2.
  3. Squaring the zero sum gives twice the sum of pairwise products as −3/2.
  4. The required sum is −3/4.