Question

Question 3: Find the principal value of cosec¯¹ (2)

Class 12 - Math - Inverse Trigonometric Functions

Answer 1

Let cosec-¹(2) = ∅
where ∅ is the principal branch of cosec-¹(2)
therefore cosec∅ = 2
since the range of principal value of branch of cosec-¹x is [+π/2,π/2] -{0}
therefore -π/2≤∅≤π/2, ∅≠0

Now cosec∅ = 2 = cosecπ/6
thus ∅ = π/6 as cosecπ/6 = 2 and
π/6 € [-π/2,π/2]-{0}