# 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