Let x=tanθ.
Then 1+x22x=sin2θ, so sin−1(sin2θ)=2θ.
And 1−x22x=tan2θ, so tan−1(tan2θ)=2θ.
Both u and v equal 2θ, so dvdu=1.
The derivative of sin−1(1+x22x) w.r.t. tan−1(1−x22x) is
Held on 4 Aug 2022 · Verified 13 Jul 2026.
21
2
1+x21−x2
1
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