RD Sharma Solutions Class 12 Maths Exercise 4.3 Chapter 4 Inverse Trigonometric Functions are provided here. These solutions help students to get familiar with the problems to analyse their conceptual understanding of the chapter. The various steps followed in solving the problems of inverse trigonometric functions are explained in brief under Exercise 4.3.
Students can primarily use the solutions as a reference guide to speed up their exam preparation. To improve their self-analysing capacity, students can download the RD Sharma Solutions Class 12 Maths Chapter 4 Inverse Trigonometric Functions Exercise 4.3 from the links given below.
RD Sharma Solutions for Class 12 Chapter 4 – Inverse Trigonometric Functions Exercise 4.3
Access answers to Maths RD Sharma Solutions for Class 12 Chapter 4 – Inverse Trigonometric Functions Exercise 4.3
Exercise 4.3 Page No: 4.14
1. Find the principal value of each of the following:
(i) tan-1 (1/√3)
(ii) tan-1 (-1/√3)
(iii) tan-1 (cos (π/2))
(iv) tan-1 (2 cos (2π/3))
Solution:
(i) Given tan-1 (1/√3)
We know that for any x ∈ R, tan-1 represents an angle in (-π/2, π/2) whose tangent is x.
So, tan-1 (1/√3) = an angle in (-π/2, π/2) whose tangent is (1/√3)
But we know that the value is equal to π/6
Therefore, tan-1 (1/√3) = π/6
Hence, the principal value of tan-1 (1/√3) = π/6
(ii) Given tan-1 (-1/√3)
We know that for any x ∈ R, tan-1 represents an angle in (-π/2, π/2) whose tangent is x.
So, tan-1 (-1/√3) = an angle in (-π/2, π/2) whose tangent is (1/√3)
But we know that the value is equal to -π/6
Therefore, tan-1 (-1/√3) = -π/6
Hence, the principal value of tan-1 (-1/√3) = – π/6
(iii) Given that tan-1 (cos (π/2))
But we know that cos (π/2) = 0
We know that for any x ∈ R, tan-1 represents an angle in (-π/2, π/2) whose tangent is x.
Therefore, tan-1 (0) = 0
Hence, the principal value of tan-1 (cos (π/2) is 0.
(iv) Given that tan-1 (2 cos (2π/3))
But we know that cos π/3 = 1/2
So, cos (2π/3) = -1/2
Therefore, tan-1 (2 cos (2π/3)) = tan-1 (2 × – ½)
= tan-1(-1)
= – π/4
Hence, the principal value of tan-1 (2 cos (2π/3)) is – π/4
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