# Inverse Trigonometric Functions Class 12 Notes Mathematics

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## Inverse Trigonometric Functions Class 12 Notes Mathematics

Download CBSE class 12th revision notes for chapter 2 Inverse Trigonometric Functions in PDF format for free. Download revision notes for Inverse Trigonometric Functions class 12 Notes and score high in exams. These are the Inverse Trigonometric Functions class 12 Notes prepared by team of expert teachers. The revision notes help you revise the whole chapter 2 in minutes. Revision notes in exam days is one of the best tips recommended by teachers during exam days.

## CBSE Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions

• The domains and ranges (principal value branches) of inverse trigonometric functions are given in the following table:
 Functions Domain Range (Principal Value Branches) [-1, 1] [-1, 1] R- [-1, 1] – {0} R-[-1, 1] R R
• should not be confused with . In fact And similarly for other trigonometric functions.
• The value of an inverse trigonometric functions which lies in its principal value branch is called the principal value of that inverse trigonometric functions.
• For suitable values of domain, we have

${\cot ^{ - 1}}{1 \over x} = {\tan ^{ - 1}}x$

$\cos e{c^{ - 1}}{1 \over x} = {\sin ^{ - 1}}x$

${\sec ^{ - 1}}{1 \over x} = {\cos ^{ - 1}}x$

${\cos ^{ - 1}}x + o{\cos ^{ - 1}}y = {\cos ^{ - 1}}\left( {xy - \sqrt {1 - {x^2}} \sqrt {1 - {y^2}} } \right)$

${\tan ^{ - 1}}x + {\tan ^{ - 1}}y + {\tan ^{ - 1}}z$ = ${\tan ^{ - 1}}\left( {{{x + y + z - xyz} \over {1 - xy - yz - zx}}} \right)$

$2{\sin ^{ - 1}}x = {\sin ^{ - 1}}\left( {2x\sqrt {1 - {x^2}} } \right)$

$2{\cos ^{ - 1}}x = {\cos ^{ - 1}}\left( {2{x^2} - 1} \right)$

$2{\tan ^{ - 1}}x = {\sin ^{ - 1}}\left( {{{2x} \over {1 + {x^2}}}} \right)$ = ${\cos ^{ - 1}}\left( {{{1 - {x^2}} \over {1 + {x^2}}}} \right) = {\tan ^{ - 1}}\left( {{{2x} \over {1 - \sqrt x }}} \right)$

$3{\sin ^{ - 1}}x = {\sin ^{ - 1}}\left( {3x - 4{x^3}} \right)$

$3{\cos ^{ - 1}}x = {\cos ^{ - 1}}\left( {4{x^3} - 3x} \right)$

$3{\tan ^{ - 1}}x = {\tan ^{ - 1}}\left( {{{3x - {x^3}} \over {1 - 3{x^2}}}} \right)$

Conversion:

• ${\sin ^{ - 1}}x = {\cos ^{ - 1}}\sqrt {1 - {x^2}}$=${\tan ^{ - 1}}{x \over {\sqrt {1 - {x^2}} }} = {\cot ^{ - 1}}{{\sqrt {1 - {x^2}} } \over x}$ = ${\sec ^{^{ - 1}}}{1 \over {\sqrt {1 - {x^2}} }} = \cos e{c^{ - 1}}{1 \over x}$
• ${\cos ^{ - 1}}x = {\sin ^{ - 1}}\sqrt {1 - {x^2}}$=${\tan ^{^{ - 1}}}{{\sqrt {1 - {x^2}} } \over x} = {\cot ^{ - 1}}{x \over {\sqrt {1 - {x^2}} }}$ = ${\sec ^{^{ - 1}}}{1 \over x} = \cos e{c^{ - 1}}{1 \over {\sqrt {1 - {x^2}} }}$
• ${\tan ^{^{ - 1}}}x = {\sin ^{ - 1}}{x \over {\sqrt {1 + {x^2}} }}$=${\cos ^{^{ - 1}}}{1 \over {\sqrt {1 + {x^2}} }} = {\sec ^{ - 1}}\sqrt {1 + {x^2}}$ = $\cos e{c^{^{ - 1}}}{{\sqrt {1 + {x^2}} } \over x} = {\cot ^{ - 1}}{1 \over x}$
• ${\cot ^{^{ - 1}}}x = {\sin ^{ - 1}}{1 \over {\sqrt {1 + {x^2}} }}$=${\cos ^{^{ - 1}}}{x \over {\sqrt {1 + {x^2}} }} = {\sec ^{ - 1}}{1 \over x}$= ${\sec ^{^{ - 1}}}{{\sqrt {1 + {x^2}} } \over x} = \cos e{c^{ - 1}}\sqrt {1 + {x^2}}$
• ${\sec ^{^{ - 1}}}x = {\tan ^{ - 1}}{{\sqrt {{x^2} - 1} } \over 1}$=${\cot ^{^{ - 1}}}{1 \over {\sqrt {{x^2} - 1} }} = {\sin ^{ - 1}}{{\sqrt {{x^2} - 1} } \over x}$ = ${\cos ^{^{ - 1}}}{1 \over x} = \cos e{c^{ - 1}}{x \over {\sqrt {{x^2} - 1} }}$
• $\cos e{c^{^{ - 1}}}x = {\sin ^{ - 1}}{1 \over x}$=${\tan ^{^{ - 1}}}{1 \over {\sqrt {{x^2} - 1} }} = {\cot ^{ - 1}}\sqrt {{x^2} - 1}$=${\sec ^{^{ - 1}}}{x \over {\sqrt {{x^2} - 1} }} = {\cos ^{ - 1}}{{\sqrt {{x^2} - 1} } \over x}$

Some other properties of Inverse Trigonometric Function:

• ${\tan ^{^{ - 1}}}{x \over {\sqrt {{a^2} - {x^2}} }} = {\sin ^{ - 1}}{x \over a}$
• ${\cot ^{^{ - 1}}}{x \over {\sqrt {{a^2} - {x^2}} }} = {\cos ^{ - 1}}{x \over a}$
• ${\tan ^{^{ - 1}}}{a \over {\sqrt {{x^2} - {a^2}} }} = \cos e{c^{ - 1}}{x \over a}$
• ${\cot ^{^{ - 1}}}{a \over {\sqrt {{x^2} - {a^2}} }} = {\sec ^{ - 1}}{x \over a}$

## CBSE Class 12 Revision Notes and Key Points

Inverse Trigonometric Functions class 12 Notes Mathematics. CBSE quick revision note for class-12 Chemistry Physics Math’s, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

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