Inverse Trigonometry System of Equations 2\tan^{-1} (\sqrt{x-x^2}) = \tan^{-1} (x) +

Halle Marsh

Halle Marsh

Answered question

2022-04-24

Inverse Trigonometry System of Equations
2tan1(xx2)=tan1(x)+tan1(1x)
I have a feeling solution includes drawing triangles but cannot make the leap to get the solution

Answer & Explanation

wellnesshaus4n4

wellnesshaus4n4

Beginner2022-04-25Added 24 answers

Take tangent of both sides (apply double angle and sum of angle formula and remember that tan(tan1y)=y
2xx21(xx2)=x+1x1x(1x)
Larry Hogan

Larry Hogan

Beginner2022-04-26Added 20 answers

We need x(1x)0x(x1)00x1
x+1x2x(1x)
Now use
arctanx+arctany=arctanx+y1xy
if xy<1
See Inverse trigonometric function identity doubt: tan1x+tan1y=π+tan1(x+y1xy), when x<0, y<0, and xy>1
OR showing arctan(23)=12arctan(125)

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