Important Questions for Class 12 Chapter 2 - Inverse Trigonometric Function

CBSE Board has laid down specific guidelines for the pattern of questions that a student of class 12th should be acquainted with. Adhering to these guidelines, we have come up with class 12th Important questions which carries questions related to all topics in Mathematics.

Important questions based on NCERT syllabus for Class 12 Chapter 2 - Inverse Trigonometric Function:

Question 1: if sin(sin^{-1} 1/5 + cos^{-1} x) = 1, Then find the valuee of x.

Solution: Given sin(sin^{-1} 1/5 + cos^{-1} x) = 1

=> sin^{-1} 1/5 + cos^{-1} x = sin^{-1}(1) [since sinθ = x => θ = sin^{-1}x ]

=> sin^{-1} 1/5 + cos^{-1} x = sin^{-1}(sin π/2) [since sin π/2 = 1]

=> sin^{-1} 1/5 + cos^{-1} x = pi/2

But we know that sin^{-1} x + cos^{-1} x = π/2

x belongs to [-1, 1]

sin^{-1} 1/5 = sin^{-1}x => x = 1/5

Question 2: Write the value of tan(2 tan^{-1} 1/5)

Solution: tan(2 tan^{-1} 1/5) = tan[tan^{-1}[(2 x 1/5)/(1-(1/5)^2)]

since 2 tan^{-1}x = tan^{-1} [ 2x/(1-x^2)]

tan[tan^{-1} (2x5/24)] = tan[tan^{-1}(5/12)] = 5/12

Question 3: Find the value of tan^{-1}[2 sin(2cos^{-1}√3/2)]

Solution: Consider tan^{-1}[2 sin(2cos^{-1}√3/2)]

tan^{-1}[2 sin(cos^{-1}(2 . 3/4 - 1))]

Since 2cos^{-1} x = cos^{-1}(2x^2 - 1)]

= tan^{-1}[2 sin{cos^{-1}(3/2 - 1)}]

= tan^{-1}[2 sin{cos^{-1}(1/2)}]

= tan^{-1}[2 sin{cos^{-1}(cos π/3)}]

= tan^{-1}[2sin π/3] [ since cos^{-1}(cos θ) = θ]

= tan^{-1}(2 . √3/2)

= tan^{-1}(√3) = tan^{-1}(tan π/3) = π/3

since tan^{-1}(tan θ) = θ