Core5 mapped NDA questions
Build the idea
Build exam-ready understanding by connecting the core idea, formulas or facts, worked example and previous NDA questions. Focus on why each rule works, then test it under timed conditions.
Concept
Inverse trigonometric functions return the angle for a given ratio, within a fixed principal-value range. They are heavily tested for their identities and principal values.
Each inverse function has a restricted range to remain single-valued.
Key Points & Formulas
- sin⁻¹x ∈ [−π/2, π/2]; cos⁻¹x ∈ [0, π]; tan⁻¹x ∈ (−π/2, π/2).
- sin⁻¹x + cos⁻¹x = π/2; tan⁻¹x + cot⁻¹x = π/2.
- tan⁻¹x + tan⁻¹y = tan⁻¹[(x+y)/(1−xy)] when xy < 1.
- sin⁻¹(−x) = −sin⁻¹x; cos⁻¹(−x) = π − cos⁻¹x.
Worked Example
Q. Evaluate sin⁻¹(1/2) + cos⁻¹(1/2).
By the identity sin⁻¹x + cos⁻¹x = π/2 for all valid x.
So the sum = π/2 (here π/6 + π/3).