Find the principal value of the following: cot - 1 ( 3 )

Let cot - 1 ( 3 ) = y cot y = 3 We know that the range of the principal value branch is ( 0 , π ) . cot y = 3 = cot π 6 ⇒ y = π 6 ∈ ( 0 , π ) Hence, the principal value of cot - 1 ( 3 ) is π 6 .

Find the principal value of the following: cot - 1 - 1 3

Let cot - 1 - 1 3 = y cot y = - 1 3 We know that the range of the principal value branch is ( 0 , π ) ⇒ y = 2 π 3 ∈ ( 0 , π ) ⇒ y = 2 π 3 ∈ ( 0 , π ) Hence, the principal value of cot - 1 - 1 3 is 2 π 3 .

Evaluate the following: cot - 1 1 3 - cosec - 1 ( - 2 ) + sec - 1 2 3

Given that, cot - 1 1 3 - cosec - 1 ( - 2 ) + sec - 1 2 3 + sec - 1 sec π 6 = cot - 1 cot π 3 + cosec - 1 cosec π 6 + sec - 1 sec π 6 = π 3 + π 6 + π 6 = 2 π 3

Evaluate the following: cot - 1 2 cos sin - 1 3 2

Given that, cot - 1 2 cos sin - 1 3 2 = cot - 1 2 cos sin - 1 sin π 3 We know that, sin - 1 sin x = x , x ∈ 0 , π . = cot - 1 2 cos π 3 = cot - 1 2 × 1 2 = cot - 1 ( 1 ) = cot - 1 cot π 4 = π 4

Evaluate the following: cosec - 1 - 2 3 + 2 cot - 1 ( - 1 ) .

Given that, cosec - 1 - 2 3 + 2 cot - 1 ( - 1 ) = cosec - 1 cosec - π 3 + 2 cot - 1 cot 3 π 4 = - π 3 + 2 × 3 π 4 = - π 3 + 3 π 2 = 7 π 6

Evaluate the following: tan - 1 - 1 3 + cot - 1 1 3 + tan - 1 sin - π 2

Given that, tan - 1 - 1 3 + cot - 1 1 3 + tan - 1 sin - π 2 = tan - 1 tan - π 6 + cot - 1 cot π 3 + tan - 1 ( - 1 ) = tan - 1 tan - π 6 + cot - 1 cot π 3 + tan - 1 tan - π 4 = - π 6 + π 3 - π 4 = - π 12

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MATHEMATICS CLASS XII VOLUME-1>Chapter 4 - Inverse Trigonometric Functions>EXERCISE

R D Sharma Solutions for Chapter: Inverse Trigonometric Functions, Exercise 1: EXERCISE

Author:R D Sharma

R D Sharma Mathematics Solutions for Exercise - R D Sharma Solutions for Chapter: Inverse Trigonometric Functions, Exercise 1: EXERCISE

Attempt the free practice questions on Chapter 4: Inverse Trigonometric Functions, Exercise 1: EXERCISE with hints and solutions to strengthen your understanding. MATHEMATICS CLASS XII VOLUME-1 solutions are prepared by Experienced Embibe Experts.