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

NDA 1 2025 Maths, question 31

Topic: Trigonometry

Passage · Q31 to Q33

Let p=sin⁡35∘p = \sin 35^{\circ}, q=sin⁡25∘q = \sin 25^{\circ} and r=sin⁡(−95∘)r = \sin\left( - 95^{\circ} \right).

Q31

What is (p+q+r)(p + q + r) equal to?

  1. (a) -1
  2. (b) 0Correct answer
  3. (c) 2sin⁡5∘2\sin 5^{\circ}
  4. (d) 2cos⁡5∘2\cos 5^{\circ}

Solution.

Answer: (b) 0

  1. Use the sum-to-product identity: p+q=2sin⁡30∘cos⁡5∘=cos⁡5∘p + q = 2\sin 30^{\circ}\cos 5^{\circ} = \cos 5^{\circ}.
  2. Also r=−sin⁡95∘=−cos⁡5∘r = - \sin 95^{\circ} = - \cos 5^{\circ}.
  3. Thus p+q+r=0p + q + r = 0.