Maths · Class 12 · Chapter 2
Inverse Trigonometric Functions
12 lessons 100 min 2 simulations
The six trigonometric functions repeat their values, so none of them is one-one on its natural domain and none has an inverse there. This chapter cuts each one down to a single stretch on which it is one-one and onto, defines the inverse on that stretch (the principal value branch), draws each inverse as the mirror image of the trimmed graph in the line y = x, and uses the two undoing rules to turn tangled expressions into simple ones.
What the exam asks
JEE Main asks for principal values, especially of negative inputs to cos⁻¹, sec⁻¹ and cot⁻¹, which land between π/2 and π rather than below zero. It asks for sin⁻¹(sin x) or tan⁻¹(tan x) with x outside the principal range, and for simplifications that start with a substitution such as x = sin θ or x = tan θ. The complementary identities such as sin⁻¹x + cos⁻¹x = π/2 and the tan⁻¹ addition rule are expected even though the rationalised text leaves them out. Marks are lost by giving an answer outside the principal range and by reading sin⁻¹x as 1/sin x.
Lessons
12 lessons · 100 min
1Why the domain is cutNCERT §2.18 min2sin⁻¹ and its principal branchNCERT §2.210 min 1 sim3cos⁻¹ and its principal branchNCERT §2.26 min4tan⁻¹ and cot⁻¹NCERT §2.27 min5cosec⁻¹ and sec⁻¹NCERT §2.27 min6The six principal branchesNCERT §2.27 min7Finding principal valuesNCERT §2.27 min8Graphs as mirror imagesNCERT §2.27 min9Undoing an inverseNCERT §2.312 min 1 sim10Simplifying by substitutionNCERT §2.38 min11Identities JEE addsNCERT §2.38 min12Chapter reviewMust-know facts, traps and formulas13 min