【ベストコレクション】 y=sin^-1(2x/1 x^2) sec^-1(1 x^2/1-x^2) 349638

Example 1 In the integral we may write = ⁡, = ⁡, = ⁡, so that the integral becomes = ⁡ ⁡ = ⁡ ( ⁡) = ⁡ ⁡ = = = ⁡ , provided For a definite integral, the bounds change once the substitution is performed and are determined using the equation = ⁡, with values in the range <

Y=sin^-1(2x/1 x^2) sec^-1(1 x^2/1-x^2)-Tan(x y) = (tan x tan y) / (1 tan x tan y) sin(2x) = 2 sin x cos x cos(2x) = cos 2 (x) sin 2 (x) = 2 cos 2 (x) 1 = 1 2 sin 2 (x) tan(2x) = 2 tan(x) / (1 This can be derived from the standard Pythagorean identity by dividing everything by cos2x, like so cos2x sin2x = 1 cos2x cos2x sin2x cos2x = 1 cos2x 1 tan2x = sec2x From this identity, we can rearrange the terms to arrive at the answer to your question tan2x = sec2x −1

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