Inverse Trigonometric Functions

Formulas are organized based on their importance in the CAT exam.
1 Domain of $$\tan^{-1}x$$
2 Principal Value of $$\tan^{-1}x$$
3 Inverse Sine of a Square-Root Expression
4 Principal Value of $$\cot^{-1}x$$
5 Inverse Cosine of a Square-Root Expression
6 Principal Value of $$\sec^{-1}x$$
7 Inverse Sine of a Tangent Expression
8 Sum of Two Inverse Cosines
9 Domain of $$\cot^{-1}x$$
10 Domain of $$\cos^{-1}x$$
11 Inverse Cosine of a Cotangent Expression
12 Domain of $$\cosec^{-1}x$$
13 Range of $$\sin^{-1}x$$
14 Inverse Sine of $$\frac{2x}{1+x^2}$$
15 Range of $$\cos^{-1}x$$
16 Range of $$\tan^{-1}x$$
17 Domain of $$\sec^{-1}x$$
18 Range of $$\sec^{-1}x$$
19 Inverse Sine of $$\frac{1-x^2}{1+x^2}$$
20 Composition of $$\sin^{-1}x$$ with $$\sin$$
21 Inverse Secant Through Cosine
22 Inverse Trigonometric Identity Using a Right Triangle
23 Inverse Cosine of a Tangent Expression
24 Odd Property of Inverse Cosecant
25 Direct Composition of $$\tan$$ and $$\tan^{-1}$$
26 Odd Property of Inverse Sine
27 Inverse Cotangent in Terms of Inverse Tangent
28 Inverse Sine of a Negative Argument
29 Inverse Sine-Cosine Complementary Relation
30 Inverse Tangent Difference Identity
31 Inverse Tangent of a Negative Reciprocal
32 Negative Argument of Inverse Cosine
33 Inverse Cotangent Reciprocal Relation
34 Composition of $$\cosec^{-1}x$$ with $$\cosec$$
35 Inverse Sine in Terms of Inverse Cosine
36 Inverse Tangent Sum for Product Greater Than One
37 Inverse Cosine of a Negative Argument
38 Inverse Cosecant of a Negative Argument
39 Sum of Two Inverse Sines
40 Negative Argument of Inverse Secant
41 Inverse Sine of a Cosine
42 Inverse Sine of Zero
43 Inverse Sine Difference Formula
44 Inverse Tangent Reciprocal Relation
45 Direct Composition of $$\cos$$ and $$\cos^{-1}$$
46 Inverse Tangent of a Cotangent
47 Inverse Cosine of a Sine
48 Double Angle Formulas for Inverse Tangent
49 Direct Composition of $$\sin$$ and $$\sin^{-1}$$
50 Inverse Cosecant Function Definition and Range
51 Inverse Tangent Difference Formula
52 Inverse Cosine of Zero
53 Inverse Secant of One
54 Composition of $$\cos^{-1}x$$ with $$\cos$$
55 Composition of $$\tan^{-1}x$$ with $$\tan$$
56 Inverse Sine of a Product
57 Inverse Sine of Minus One
58 Inverse Tangent of a Difference of Fractions
59 Inverse Cosecant Through Sine
60 Inverse Tangent of a Sum of Fractions
61 Inverse Tangent-Cotangent Complementary Relation
62 Inverse Tangent Sum When Product Equals One
63 Odd Property of Inverse Tangent
64 Inverse Tangent of a Reciprocal
65 Inverse Cotangent of a Tangent
66 Composition of $$\cot^{-1}x$$ with $$\cot$$
67 Derivative of Inverse Sine
68 Three-Term Inverse Tangent Identity for Product Relation
69 Inverse Cotangent at Negative Infinity
70 Derivative of Inverse Cosecant
71 Inverse Tangent of a Negative Argument
72 Inverse Secant in Terms of Inverse Cosecant
73 Derivative of Inverse Cosine
74 Derivative with Chain Rule: $$\cot^{-1}u$$
75 Derivative of Inverse Cotangent
76 Inverse Cotangent of a Reciprocal
77 Inverse Cotangent of Zero
78 Integral of $$\frac{-1}{\sqrt{1-x^2}}$$
79 Inverse Cosecant of One
80 Integral of $$\frac{-1}{1+x^2}$$
81 Inverse Cosine of One
82 Inverse Cosine of Minus One
83 Inverse Tangent at Negative Infinity
84 Inverse Cosecant at Positive Infinity
85 Derivative of Inverse Tangent
86 Inverse Cosine with Linear Argument
87 Range of $$\cosec^{-1}x$$
88 Inverse Cosine of $$\frac{2x}{1+x^2}$$
89 Three-Term Inverse Tangent Identity
90 Inverse Secant Function Definition and Range
91 Inverse Cotangent with Linear Argument
92 Inverse Tangent Function Definition and Range
93 Principal Value of $$\cos^{-1}\left(\frac12\right)$$
94 Inverse Sine and Inverse Cotangent Relation
95 Integral of Inverse Tangent
96 Inverse Cosine and Inverse Tangent Relation
97 Tangent Half-Angle Substitution
98 Integral of Inverse Sine
99 Integral of Inverse Cosecant
100 Principal Value of $$\tan^{-1}1$$
101 Inverse Tangent with Linear Argument
102 Inverse Sine and Inverse Tangent Relation
103 Relation Between $$\sin^{-1}x$$ and $$\tan^{-1}x$$
104 Principal Value of $$\cos^{-1}\left(\frac{\sqrt3}{2}\right)$$
105 Negative Argument Formulas
106 Relation Between $$\tan^{-1}x$$ and $$\cos^{-1}x$$
107 Principal Value of $$\sin^{-1}\left(\frac12\right)$$
108 Inverse Tangent from Half-Angle Substitution
109 Principal Value of $$\cot^{-1}\sqrt3$$
110 Principal Value of $$\tan^{-1}\sqrt3$$
111 Relation Between $$\cot^{-1}x$$ and $$\sin^{-1}x$$
112 Principal Value of $$\cosec^{-1}(-2)$$
113 Inverse Cosine Sum Special Case
114 Inverse Cosecant Negative-Argument Relation
115 Inverse Sine Sum Special Case
116 Inverse Cotangent Sum Special Case
117 Relation Between $$\cot^{-1}x$$ and $$\cos^{-1}x$$
118 Periodic Reduction for $$\tan^{-1}(\tan x)$$
119 Periodic Reduction for $$\cot^{-1}(\cot x)$$
120 Inverse Secant Negative-Argument Relation
121 Principal-Value Rule for $$\tan^{-1}(\tan x)$$
122 Principal-Value Rule for $$\sin^{-1}(\sin x)$$
123 Principal-Value Rule for $$\cos^{-1}(\cos x)$$
124 General Solution of $$\sin x=a$$
125 General Solution of $$\cos x=a$$
126 Principal-Value Rule for $$\cot^{-1}(\cot x)$$
127 General Solution of $$\tan x=a$$
128 Inverse Cosecant and Secant Relation
129 Range-Based Rule for $$\cos^{-1}(\cos x)$$
130 Logarithmic Form of the Standard Radical Integral
131 Inverse Sine with Linear Argument
132 Inverse Secant and Cosecant Relation
133 Principal Value of $$\cot^{-1}1$$
134 Principal Value of $$\cos^{-1}x$$
135 Difference of Two Inverse Tangents
136 Principal Value of $$\cosec^{-1}x$$
137 Inverse Tangent of a Sine Expression
138 Principal Value of $$\sin^{-1}x$$
139 Inverse Tangent of $$\frac{2x}{1-x^2}$$
140 Principal Value of $$\cot^{-1}(-1)$$
141 Principal Value of $$\sec^{-1}2$$
142 Principal Value of $$\cosec^{-1}2$$
143 Inverse Tangent Sum Special Case
144 Inverse Tangent in Terms of Inverse Cotangent
145 General Solution of $$\sec x=a$$
146 Integral of $$\frac1{|x|\sqrt{x^2-1}}$$
147 Integral of Inverse Cosine
148 Inverse Secant at Positive Infinity
149 Negative Argument of Inverse Cotangent
150 Inverse Sine Addition Formula
151 Inverse Cotangent of a Negative Argument
152 Inverse Tangent of $$\frac{1}{1+x^2}$$
153 Derivative of Inverse Secant
154 Cosine Half-Angle Substitution
155 General Solution of $$\cot x=a$$
156 Inverse Tangent of a Rationalized Form
157 Inverse Cosine Difference Formula
158 Derivative with Chain Rule: $$\cos^{-1}u$$
159 Inverse Tangent Addition Formula
160 Derivative with Chain Rule: $$\tan^{-1}u$$
161 Inverse Tangent Sum for Product Less Than One
162 Inverse Cosine Through Sine Complement
163 Derivative with Chain Rule: $$\sin^{-1}u$$
164 Range of $$\cot^{-1}x$$
165 Inverse Sine of a Rationalized Form
166 Principal Value of $$\cos^{-1}\left(-\frac12\right)$$
167 Inverse Tangent Triple-Angle Formula
168 Inverse Secant of a Negative Argument
169 Tangent in Half-Angle Substitution
170 Principal Value of $$\tan^{-1}(-1)$$
171 Differential Form of Half-Angle Substitution
172 Relation Between $$\tan^{-1}x$$ and $$\sin^{-1}x$$
173 Sum of Two Inverse Tangents
174 Integral of $$\frac1{1+x^2}$$
175 Principal Value of $$\sin^{-1}\left(-\frac12\right)$$
176 Inverse Cosine Function Definition and Range
177 Inverse Tangent Double-Angle Formula
178 Inverse Cosine of a Rationalized Form
179 Principal Value of $$\sin^{-1}\left(\frac{\sqrt3}{2}\right)$$
180 Relation Between $$\cos^{-1}x$$ and $$\tan^{-1}x$$
181 General Solution of $$\cosec x=a$$
182 Inverse Cosine of $$\frac{1-x^2}{1+x^2}$$
183 Inverse Sine of One
184 Principal Value of $$\sec^{-1}(-2)$$
185 Composition of $$\sec^{-1}x$$ with $$\sec$$
186 Inverse Sine Function Definition and Range
187 Range-Based Sign Rule for $$\sin^{-1}(\sin x)$$
188 Integral of $$\frac{-1}{|x|\sqrt{x^2-1}}$$
189 Relation between Inverse Secant and Cosecant
190 Integral of $$\frac1{\sqrt{1-x^2}}$$
191 Relation between Inverse Tangent and Cotangent
192 Relation between Inverse Sine and Cosine
193 Integral of Inverse Cotangent
194 Inverse Sine of a Cotangent Expression
195 Inverse Trigonometric Principal-Value Rule
196 Inverse Tangent Difference as a Single Fraction
197 Inverse Cosine Addition Formula
198 Inverse Tangent at Infinity
199 Inverse Tangent of Zero
200 Inverse Cosine in Terms of Inverse Sine
201 Inverse Cotangent Function Definition and Range
202 Inverse Cosine and Inverse Cotangent Relation
203 Inverse Cosecant in Terms of Inverse Secant
204 Derivative with Chain Rule: $$\sec^{-1}u$$
205 Inverse Secant-Cosecant Complementary Relation
206 Inverse Cotangent at Infinity
207 Domain of $$\sin^{-1}x$$
208 Derivative with Chain Rule: $$\cosec^{-1}u$$
209 Integral of Inverse Secant