Prove that : sin cot - 1 cos tan - 1 x = x 2 + 1 x 2 + 2 .

We need to prove that, sin cot - 1 cos tan - 1 x = x 2 + 1 x 2 + 2 Taking L . H . S . = sin cot - 1 cos tan - 1 x Let tan - 1 x = θ ⇒ tan θ = x 1 Using Pythagoras theorem A C 2 = A B 2 + B C 2 A C 2 = 1 2 + x 2 A C 2 = 1 + x 2 A C = 1 + x 2 We know that, ⇒ cos θ = B H y = 1 1 + x 2 ⇒ sin θ = P H y = x 1 + x 2 ⇒ sin cot - 1 cos θ ⇒ sin cot - 1 1 1 + x 2 Let cot - 1 1 1 + x 2 = y ⇒ cot y = 1 1 + x 2 = B P Using Pythagoras theorem A C 2 = A B 2 + B C 2 A C 2 = 1 2 + 1 + x 2 2 A C 2 = 1 + 1 + x 2 A C 2 = 2 + x 2 A C = 2 + x 2 ⇒ sin y = P H y = 1 + x 2 2 + x 2 = R . H . S . sin cot - 1 cos tan - 1 x = x 2 + 1 x 2 + 2 . Hence proved.

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Understanding ISC Mathematics Class 12 Volume 1>Chapter 2 - Inverse Trigonometric Functions>EXERCISE 2.2

M L Aggarwal Solutions for Chapter: Inverse Trigonometric Functions, Exercise 2: EXERCISE 2.2

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Inverse Trigonometric Functions, Exercise 2: EXERCISE 2.2

Attempt the practice questions on Chapter 2: Inverse Trigonometric Functions, Exercise 2: EXERCISE 2.2 with hints and solutions to strengthen your understanding. Understanding ISC Mathematics Class 12 Volume 1 solutions are prepared by Experienced Embibe Experts.