Answer:
formulas:
Step-by-step explanation:
Inverse Trigonometric Formulas List
S.No Inverse Trigonometric Formulas
8 tan-1x + cot-1x = π/2 , x ∈ R
9 sec-1x + cosec-1x = π/2 ,|x| ≥ 1
10 sin-1(1/x) = cosec-1(x), if x ≥ 1 or x ≤ -1
11 cos-1(1/x) = sec-1(x), if x ≥ 1 or x ≤ -1
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 cosec-1(-x) = -cosec-1(x), |x| ≥ 1
5 sec-1(-x) = π -sec-1(x), |x| ≥ 1
6 cot-1(-x) = π – cot-1(x), x ∈ R
7 sin-1x + cos-1x = π/2 , x ∈ [-1, 1]
12 tan-1(1/x) = cot-1(x), x > 0
13 tan-1 x + tan-1 y = tan-1((x+y)/(1-xy)), if the value xy < 1
14 tan-1 x – tan-1 y = tan-1((x-y)/(1+xy)), if the value xy > -1
15 2 tan-1 x = sin-1(2x/(1+x2)), |x| ≤ 1
16 2tan-1 x = cos-1((1-x2)/(1+x2)), x ≥ 0
17 2tan-1 x = tan-1(2x/(1-x2)), -1<x<1
18 3sin-1x = sin-1(3x-4x3)
19 3cos-1x = cos-1(4x3-3x)
20 3tan-1x = tan-1((3x-x3)/(1-3x2))
21 sin(sin-1(x)) = x, -1≤ x ≤1
22 cos(cos-1(x)) = x, -1≤ x ≤1
23 tan(tan-1(x)) = x, – ∞ < x < ∞.
24 cosec(cosec-1(x)) = x, – ∞ < x ≤ 1 or -1 ≤ x < ∞
25 sec(sec-1(x)) = x,- ∞ < x ≤ 1 or 1 ≤ x < ∞
26 cot(cot-1(x)) = x, – ∞ < x < ∞.
27 sin-1(sin θ) = θ, -π/2 ≤ θ ≤π/2
28 cos-1(cos θ) = θ, 0 ≤ θ ≤ π
29 tan-1(tan θ) = θ, -π/2 < θ < π/2
30 cosec-1(cosec θ) = θ, – π/2 ≤ θ < 0 or 0 < θ ≤ π/2
31 sec-1(sec θ) = θ, 0 ≤ θ ≤ π/2 or π/2< θ ≤ π
32 cot-1(cot θ) = θ, 0 < θ < π
33 sin−1x+sin−1y=sin−1(x1−y2−−−−−√+y1−x2−−−−−√),ifx,y≥0andx2+y2≤1
34 sin−1x+sin−1y=π−sin−1(x1−y2−−−−−√+y1−x2−−−−−√), if x, y ≥ 0 and x2+y2>1.
35 sin−1x−sin−1y=π−sin−1(x1−y2−−−−−√−y1−x2−−−−−√), if x, y ≥ 0 and x2+y2≤1.
36 sin−1x−sin−1y=π−sin−1(x1−y2−−−−−√−y1−x2−−−−−√), if x, y ≥ 0 and x2 +y2>1.
37 cos−1x+cos−1y=cos−1(xy−1−x2−−−−−√1−y2−−−−−√), if x,
y >0 and x2+y2 ≤1.
38 cos−1x+cos−1y=π−cos−1(xy−1−x2−−−−−√1−y2−−−−−√), if x, y >0 and x2+y2>1.
39 cos−1x−cos−1y=cos−1(xy+1−x2−−−−−√1−y2−−−−−√), if x, y > 0 and x2+y2≤1.
40 cos−1x−cos−1y=π−cos−1(xy+1−x2−−−−−√1−y2−−−−−√),if x, y > 0 and x2 +y2>1.
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Answers & Comments
Answer:
formulas:
Step-by-step explanation:
Inverse Trigonometric Formulas List
S.No Inverse Trigonometric Formulas
8 tan-1x + cot-1x = π/2 , x ∈ R
9 sec-1x + cosec-1x = π/2 ,|x| ≥ 1
10 sin-1(1/x) = cosec-1(x), if x ≥ 1 or x ≤ -1
11 cos-1(1/x) = sec-1(x), if x ≥ 1 or x ≤ -1
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 cosec-1(-x) = -cosec-1(x), |x| ≥ 1
5 sec-1(-x) = π -sec-1(x), |x| ≥ 1
6 cot-1(-x) = π – cot-1(x), x ∈ R
7 sin-1x + cos-1x = π/2 , x ∈ [-1, 1]
8 tan-1x + cot-1x = π/2 , x ∈ R
9 sec-1x + cosec-1x = π/2 ,|x| ≥ 1
10 sin-1(1/x) = cosec-1(x), if x ≥ 1 or x ≤ -1
11 cos-1(1/x) = sec-1(x), if x ≥ 1 or x ≤ -1
12 tan-1(1/x) = cot-1(x), x > 0
13 tan-1 x + tan-1 y = tan-1((x+y)/(1-xy)), if the value xy < 1
14 tan-1 x – tan-1 y = tan-1((x-y)/(1+xy)), if the value xy > -1
15 2 tan-1 x = sin-1(2x/(1+x2)), |x| ≤ 1
16 2tan-1 x = cos-1((1-x2)/(1+x2)), x ≥ 0
17 2tan-1 x = tan-1(2x/(1-x2)), -1<x<1
18 3sin-1x = sin-1(3x-4x3)
19 3cos-1x = cos-1(4x3-3x)
20 3tan-1x = tan-1((3x-x3)/(1-3x2))
21 sin(sin-1(x)) = x, -1≤ x ≤1
22 cos(cos-1(x)) = x, -1≤ x ≤1
23 tan(tan-1(x)) = x, – ∞ < x < ∞.
24 cosec(cosec-1(x)) = x, – ∞ < x ≤ 1 or -1 ≤ x < ∞
25 sec(sec-1(x)) = x,- ∞ < x ≤ 1 or 1 ≤ x < ∞
26 cot(cot-1(x)) = x, – ∞ < x < ∞.
27 sin-1(sin θ) = θ, -π/2 ≤ θ ≤π/2
28 cos-1(cos θ) = θ, 0 ≤ θ ≤ π
29 tan-1(tan θ) = θ, -π/2 < θ < π/2
30 cosec-1(cosec θ) = θ, – π/2 ≤ θ < 0 or 0 < θ ≤ π/2
31 sec-1(sec θ) = θ, 0 ≤ θ ≤ π/2 or π/2< θ ≤ π
32 cot-1(cot θ) = θ, 0 < θ < π
33 sin−1x+sin−1y=sin−1(x1−y2−−−−−√+y1−x2−−−−−√),ifx,y≥0andx2+y2≤1
34 sin−1x+sin−1y=π−sin−1(x1−y2−−−−−√+y1−x2−−−−−√), if x, y ≥ 0 and x2+y2>1.
35 sin−1x−sin−1y=π−sin−1(x1−y2−−−−−√−y1−x2−−−−−√), if x, y ≥ 0 and x2+y2≤1.
36 sin−1x−sin−1y=π−sin−1(x1−y2−−−−−√−y1−x2−−−−−√), if x, y ≥ 0 and x2 +y2>1.
37 cos−1x+cos−1y=cos−1(xy−1−x2−−−−−√1−y2−−−−−√), if x,
y >0 and x2+y2 ≤1.
38 cos−1x+cos−1y=π−cos−1(xy−1−x2−−−−−√1−y2−−−−−√), if x, y >0 and x2+y2>1.
39 cos−1x−cos−1y=cos−1(xy+1−x2−−−−−√1−y2−−−−−√), if x, y > 0 and x2+y2≤1.
40 cos−1x−cos−1y=π−cos−1(xy+1−x2−−−−−√1−y2−−−−−√),if x, y > 0 and x2 +y2>1.