If tan - 1 x + tan - 1 y = π 4 , then write the value of x + y + x y .

Given: tan - 1 x + tan - 1 y = π 4 We know that, tan - 1 x + tan - 1 y = tan - 1 x + y 1 - x y . Now, tan - 1 x + tan - 1 y = π 4 ⇒ tan - 1 x + y 1 - x y = π 4 ⇒ x + y 1 - x y = tan π 4 ⇒ x + y 1 - x y = 1 ⇒ x + y = 1 - x y ⇒ x + y + x y = 1 ∴ x + y + x y = 1 .

Write the value of sin - 1 cos π 9 .

Consider, sin - 1 cos π 9 = sin - 1 sin π 2 - π 9 ∵ cos x = sin π 2 - x = sin - 1 sin 7 π 18 = 7 π 18 ∵ sin - 1 ( sin x ) = x ∴ sin - 1 cos π 9 = 7 π 18

Write the value of sin π 3 - sin - 1 - 1 2 .

We have sin π 3 - sin - 1 - 1 2 = sin π 3 - - π 6 = sin π 3 + π 6 = sin π 2 = 1 ∴ sin π 3 - sin - 1 - 1 2 = 1

Write the value of tan - 1 tan 15 π 4 .

We have tan - 1 tan 15 π 4 = tan - 1 tan 4 π - π 4 tan - 1 - tan π 4 [ ∵ tan ( 4 π - x ) = - tan x ] = tan - 1 tan - π 4 = - π 4 ∵ tan - 1 ( tan x ) = x ∴ tan - 1 tan 15 π 4 = - π 4

Write the value of 2 sin - 1 1 2 + cos - 1 - 1 2 .

Given that, 2 sin - 1 1 2 + cos - 1 - 1 2 = sin - 1 2 × 1 2 1 - 1 2 2 + cos - 1 - 1 2 = sin - 1 3 2 + cos - 1 - 1 2 = sin - 1 sin π 3 + cos - 1 cos 2 π 3 We know that, sin - 1 sin x = x where x ∈ - π 2 , π 2 and cos - 1 cos x = x , where x ∈ 0 , π = π 3 + 2 π 3 = π

Write the value of tan - 1 a b - tan - 1 a - b a + b .

We know that tan - 1 x - tan - 1 y = tan - 1 x - y 1 + x y . Now, tan - 1 a b - tan - 1 a - b a + b = tan - 1 a b - a - b a + b 1 + a b a - b a + b = tan - 1 a 2 + a b - a b + b 2 b ( a + b ) a b + b 2 - a b + a 2 b ( a + b ) = tan - 1 ( 1 ) = tan - 1 tan π 4 ∵ tan π 4 = 1 = π 4 ∴ tan - 1 a b - tan - 1 a - b a + b = π 4

Write the value of cos - 1 cos 5 π 4 .

cos - 1 cos 5 π 4 ≠ 5 π 4 as 5 π 4 does not lie between 0 and π . We have cos - 1 cos 5 π 4 = cos - 1 cos 2 π - 3 π 4 = cos - 1 cos 3 π 4 = 3 π 4

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MATHEMATICS CLASS XII VOLUME-1>Chapter 4 - Inverse Trigonometric Functions>MULTIPLE CHOICE QUESTIONS (MCQs)

R D Sharma Solutions for Chapter: Inverse Trigonometric Functions, Exercise 1: MULTIPLE CHOICE QUESTIONS (MCQs)

Author:R D Sharma

R D Sharma Mathematics Solutions for Exercise - R D Sharma Solutions for Chapter: Inverse Trigonometric Functions, Exercise 1: MULTIPLE CHOICE QUESTIONS (MCQs)

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