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Finding principal value

Principal Value

Example 1 Important

Ex 2.1, 1

Ex 2.1, 3

Ex 2.1, 10 Important

Ex 2.1, 2

Ex 2.1, 5 Important

Ex 2.1, 9

Ex 2.1, 7 Important

Ex 2.1, 4 Important

Ex 2.1, 6

Ex 2.1, 8 Important

Example 2

Ex 2.2, 10

Example 6 Important

Ex 2.2, 8 You are here

Ex 2.2, 11

Misc 2 Important

Ex 2.2, 13 (MCQ) Important

Misc 1

Ex 2.2, 14 (MCQ) Important

Ex 2.2, 15 (MCQ)

Ex 2.1, 12 Important

Ex 2.1, 14 (MCQ) Important

Ex 2.1, 11 Important

Chapter 2 Class 12 Inverse Trigonometric Functions

Concept wise

Last updated at May 29, 2023 by Teachoo

Ex 2.2, 8 Find the value of tan-1 ["2 cos " (2"sinβ1" 1/2)] Solving sin-1 (π/π) Let y = sin-1 (1/2) sin y = 1/2 sin y = sin (π /π) Range of principal value of sin β1 is [(βπ)/2, ( π)/2] Hence, y = π /π Rough We know that sin 30Β° = 1/2 ΞΈ = 30Β° = 30 Γ π/180 = π/6 Since 1/2 is positive Principal value is ΞΈ i.e. π /π Now solving tan-1 ["2 cos " (2"sinβ1" 1/2)] = tan-1 ["2 cos " (2 Γ π/6)] = tan-1 ["2 cos" π /π] = tan-1 ["2" Γπ/π] = tan-1 [1] = tan-1 [πππ§β‘γπ /πγ ] = π /π (Since cosπ/3 = 1/2)