Inverse Trigonometric Functions Class 12 Maths Notes – Formulas & Quick Revision

Inverse Trig Functions mein principal values aur inverse identities aate hain — chhota par precise chapter. Yahan aapko is chapter ke sabse important formulas aur quick revision points free milte hain — NCERT/CBSE syllabus ke hisaab se, boards aur JEE/NEET dono ke liye.

Important Formulas & Concepts — Inverse Trigonometric Functions

• sin⁻¹x: domain [−1,1], range [−π/2, π/2]
• cos⁻¹x: range [0, π]; tan⁻¹x: range (−π/2, π/2)
• sin⁻¹x + cos⁻¹x = π/2
• tan⁻¹x + cot⁻¹x = π/2
• sin⁻¹(−x) = −sin⁻¹x; cos⁻¹(−x) = π − cos⁻¹x
• tan⁻¹x + tan⁻¹y = tan⁻¹[(x+y)/(1−xy)] (xy < 1)
• 2tan⁻¹x = sin⁻¹(2x/(1+x²)) = cos⁻¹((1−x²)/(1+x²))
• sin(sin⁻¹x) = x, par sin⁻¹(sinx) = x sirf principal range mein

Quick Revision Points

• Principal value ranges ratna sabse zaroori hai
• sin⁻¹(sin 2π/3) = π/3 (2π/3 nahi!) — range adjust karo
• Substitution x = tanθ ya sinθ se simplification hoti hai
• Rationalised syllabus mein ye chapter chhota ho gaya hai
• Domain restrictions dhyan se dekho

FAQ

Principal values mein galti hoti hai?

PDF mein ranges ka ek visual chart hai — quadrant ke saath yaad ho jata hai.

Boards mein kya aata hai?

Principal values aur simplification — 2-4 marks.

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