find inverse of the function sec inverse x in there receptive domain
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Step-by-step explanation:
S.NoInverse Trigonometric Formulas1sin-1(-x) = -sin-1(x), x ∈ [-1, 1]2cos-1(-x) = π -cos-1(x), x ∈ [-1, 1]3tan-1(-x) = -tan-1(x), x ∈ R4cosec-1(-x) = -cosec-1(x), |x| ≥ 15sec-1(-x) = π -sec-1(x), |x| ≥ 16cot-1(-x) = π – cot-1(x), x ∈ R7sin-1x + cos-1x = π/2 , x ∈ [-1, 1]8tan-1x + cot-1x = π/2 , x ∈ R9sec-1x + cosec-1x = π/2 ,|x| ≥ 110sin-1(1/x) = cosec-1(x), if x ≥ 1 or x ≤ -111cos-1(1/x) = sec-1(x), if x ≥ 1 or x ≤ -112tan-1(1/x) = cot-1(x), x > 013tan-1 x + tan-1 y = tan-1((x+y)/(1-xy)), if the value xy < 114tan-1 x – tan-1 y = tan-1((x-y)/(1+xy)), if the value xy > -1152 tan-1 x = sin-1(2x/(1+x2)), |x| ≤ 1162tan-1 x = cos-1((1-x2)/(1+x2)), x ≥ 0172tan-1 x = tan-1(2x/(1-x2)), -1<x<1183sin-1x = sin-1(3x-4x3)193cos-1x = cos-1(4x3-3x)203tan-1x = tan-1((3x-x3)/(1-3x2))21sin(sin-1(x)) = x, -1≤ x ≤122cos(cos-1(x)) = x, -1≤ x ≤123tan(tan-1(x)) = x, – ∞ < x < ∞.24cosec(cosec-1(x)) = x, – ∞ < x ≤ 1 or -1 ≤ x < ∞25sec(sec-1(x)) = x,- ∞ < x ≤ 1 or 1 ≤ x < ∞26cot(cot-1(x)) = x, – ∞ < x < ∞.27sin-1(sin θ) = θ, -π/2 ≤ θ ≤π/228cos-1(cos θ) = θ, 0 ≤ θ ≤ π29tan-1(tan θ) = θ, -π/2 < θ < π/230cosec-1(cosec θ) = θ, – π/2 ≤ θ < 0 or 0 < θ ≤ π/231sec-1(sec θ) = θ, 0 ≤ θ ≤ π/2 or π/2< θ ≤ π32cot-1(cot θ) = θ, 0 < θ < π33sin−1x+sin−1y=sin−1(x1−y2−−−−−√+y1−x2−−−−−√),ifx,y≥0andx2+y2≤134sin−1x+sin−1y=π−sin−1(x1−y2−−−−−√+y1−x2−−−−−√), if x, y ≥ 0 and x2+y2>1.35sin−1x−sin−1y=π−sin−1(x1−y2−−−−−√−y1−x
Step-by-step explanation:
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