Ch 2 covers inverse trigonometric functions — the "reverse" of trig functions. Students learn principal value branches, properties, and how to simplify complex inverse trig expressions.
sin⁻¹: [−1,1] → [−π/2, π/2]. cos⁻¹: [−1,1] → [0, π]. tan⁻¹: ℝ → (−π/2, π/2). These restricted ranges ensure the inverses are functions (one output per input).
sin⁻¹x + cos⁻¹x = π/2. tan⁻¹x + cot⁻¹x = π/2. sec⁻¹x + cosec⁻¹x = π/2. tan⁻¹x + tan⁻¹y = tan⁻¹[(x+y)/(1−xy)] when xy < 1. 2tan⁻¹x = sin⁻¹(2x/(1+x²)) = cos⁻¹((1−x²)/(1+x²)).
Download: https://ncert.nic.in/textbook/pdf/lemh102.pdf | Complete book Part I: https://ncert.nic.in/textbook/pdf/lemh1ps.zip
Trig functions are periodic and not one-one over their entire domain. To define an inverse, we restrict the range to a principal value branch where the original function is one-one and onto, ensuring each input gives exactly one output.
Book a Trial + Diagnostic session. Get a personalized Learning Path with clear milestones, tutor match, and a plan recommendation — all within 24 hours.
Book Trial + Diagnostic →