Inverse Trigonometric Functions

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