CBSE Class 12 Mathematics 2026 Main Paper 65/1/3 · Q212 Marksinverse_trigonometric_functions
CBSE Class 12 Mathematics 2026 Main Paper 65/1/3 · Question 21 (Inverse Trigonometric Functions)
Simplify: tan⁻¹( (cos2x − sin2x)/(cos2x + sin2x) ), 0 < x < π/4. OR Evaluate: tan( sin⁻¹1 − cos⁻¹(−1/2) ).
Alternative 1 2 Marks
Simplify: tan⁻¹( (cos2x − sin2x)/(cos2x + sin2x) ), 0 < x < π/4.
Answer: π/4 − 2x
- Divide numerator and denominator by cos2x: (1 − tan2x)/(1 + tan2x).
- = tan(π/4 − 2x). Since 0<x<π/4, π/4−2x ∈ (−π/4, π/4), so tan⁻¹(tan(π/4−2x)) = π/4−2x.
- π/4 − 2x
Alternative 2 2 Marks
Evaluate: tan( sin⁻¹1 − cos⁻¹(−1/2) ).
Answer: −1/√3
- sin⁻¹1 = π/2.
- cos⁻¹(−1/2) = 2π/3. Difference = π/2 − 2π/3 = −π/6. tan(−π/6) = −1/√3.
- −1/√3