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NDA 2 2024 Maths, question 30

Topic: Trigonometry

Q30

What is cos⁡17∘−sin⁡17∘cos⁡17∘+sin⁡17∘\frac{\cos 17^{\circ}-\sin 17^{\circ}}{\cos 17^{\circ}+\sin 17^{\circ}} equal to?

  1. (a) tan⁡34∘\tan 34^{\circ}
  2. (b) cot⁡34∘\cot 34^{\circ}
  3. (c) tan⁡62∘\tan 62^{\circ}
  4. (d) cot⁡62∘\cot 62^{\circ}Correct answer

Solution.

Answer: (d) cot⁡62∘\cot 62^{\circ}

  1. Divide numerator and denominator by cos17°.
  2. The ratio becomes (1−tan17°)/(1+tan17°)=tan(45°−17°)=tan28°=cot62°.