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

NDA 2 2024 Maths, question 79

Topic: Differential calculus

Q79

What is lim⁡x→π2(sec⁡θ−tan⁡θ)\underset{x\to \frac{\pi}{2}}{\lim }(\sec \theta-\tan \theta) equal to?

  1. (a) −1-1
  2. (b) 00Correct answer
  3. (c) 1/21/2
  4. (d) 11

Solution.

Answer: (b) 00

  1. Read the limit as θ→π2\theta \to \frac{\pi}{2}.
  2. sec⁡θ−tan⁡θ=1−sin⁡θcos⁡θ=cos⁡θ1+sin⁡θ\sec\theta - \tan\theta = \frac{1 - \sin\theta}{\cos\theta} = \frac{\cos\theta}{1 + \sin\theta}.
  3. At θ=π2\theta = \frac{\pi}{2} this is 02=0\frac{0}{2} = 0.

Trap: The paper writes x→π2x \to \frac{\pi}{2} under the limit while the expression uses θ\theta; it is a misprint for θ\theta.