S.No
Inverse Trigonometry Class 12 Formulas
1
sin-1 (-x) = -sin-1(x), x ∈ [-1, 1]
2
cos-1(-x) = π -cos-1(x), x ∈ [-1, 1]
3
tan-1(-x) = -tan-1(x), x ∈ R
4
cot-1(-x) = π – cot-1(x), x ∈ R
5
sec-1(-x) = π -sec-1(x), |x| ≥ 1
6
cosec-1(-x) = -cosec-1(x), |x| ≥ 1
7
sin-1x + cos-1x = π/2 , x ∈ [-1, 1]
8
sin-1(1/x) = cosec-1(x), if x ≥ 1 or x ≤ -1
9
cos-1(1/x) = sec-1(x), if x ≥ 1 or x ≤ -1
10
tan-1x + cot-1x = π/2 , x ∈ R
11
tan-1(1/x) = cot-1(x), x > 0
12
tan-1 x + tan-1 y = tan-1((x+y)/(1-xy)), if the value xy < 1
13
tan-1 x – tan-1 y = tan-1((x-y)/(1+xy)), if the value xy > -1
14
2 tan-1 x = sin-1(2x/(1+x2)), |x| ≤ 1
15
sec-1x + cosec-1x = π/2 ,|x| ≥ 1
16
3sin-1x = sin-1(3x-4x3)
17
sin(sin-1(x)) = x, -1≤ x ≤1
18
3cos-1x = cos-1(4x3-3x)
19
cos(cos-1(x)) = x, -1≤ x ≤1
20
3tan-1x = tan-1((3x-x3)/(1-3x2)
21
tan(tan-1(x)) = x, – ∞ < x < ∞
22
sec(sec-1(x)) = x,- ∞ < x ≤ 1 or 1 ≤ x < ∞
23
cosec(cosec-1(x)) = x, – ∞ < x ≤ 1 or -1 ≤ x < ∞
24
cot(cot-1(x)) = x, – ∞ < x < ∞
25
sin-1(sin θ) = θ, -π/2 ≤ θ ≤π/2
26
cos-1(cos θ) = θ, 0 ≤ θ ≤ π
27
tan-1(tan θ) = θ, -π/2 < θ < π/2
28
sec-1(sec θ) = θ, 0 ≤ θ ≤ π/2 or π/2< θ ≤ π
29
cosec-1(cosec θ) = θ, – π/2 ≤ θ < 0 or 0 < θ ≤ π/2
30
cot-1(cot θ) = θ, 0 < θ < π