Master Inverse Trigonometric Functions (Class 12 Maths Chapter 2) – Formulas, NCERT Solutions & CBSE PYQs
Chapter 2: Inverse Trigonometric Functions (Class 12 CBSE Math) ✅ A. Key Concepts & Formulas Definition & Principal Values Inverse trig functions are the restricted inverses of trig functions: sin − 1 x \sin^{-1} x : domain x ∈ [ − 1 , 1 ] x \in [-1,1] ; range [ − π / 2 , π / 2 ] [-π/2, π/2] cos − 1 x \cos^{-1} x : domain [ − 1 , 1 ] [-1,1] ; range [ 0 , π ] [0, π] tan − 1 x \tan^{-1} x : domain all real; range ( − π / 2 , π / 2 ) (-π/2, π/2) Similar definitions apply for cot − 1 , sec − 1 , csc − 1 \cot^{-1}, \sec^{-1}, \csc^{-1} . Properties & Identities Odd–even behavior: sin − 1 ( − x ) = − sin − 1 x \sin^{-1}(-x)=-\sin^{-1}x , cos − 1 ( − x ) = π − cos − 1 x \cos^{-1}(-x)=π-\cos^{-1}x , etc. Complementary relations: sin − 1 x + cos − 1 x = π / 2 \sin^{-1}x + \cos^{-1}x = π/2 ; tan − 1 x + cot − 1 x = π / 2 \tan^{-1}x + \cot^{-1}x = π/2 . Reciprocal links: sin − 1 ( 1 / a ) = csc − 1 ( a ) \sin^{-1}(1/a)...