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

NDA 1 2024 Maths, question 39

Topic: Trigonometry

Q39

If cos⁡−1x=sin⁡−1x\cos ^{-1}x=\sin ^{-1}x, then which one of the following is correct ?

  1. (a) x=1x=1
  2. (b) x=12x=\frac{1}{2}
  3. (c) x=12x=\frac{1}{\sqrt{2}}Correct answer
  4. (d) x=13x=\frac{1}{\sqrt{3}}

Solution.

Answer: (c) x=12x=\frac{1}{\sqrt{2}}

  1. For principal inverse functions, sin⁻¹x + cos⁻¹x = π/2.
  2. Equality of the two inverse values makes each π/4, hence x = sin(π/4) = 1/√2.