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Class 12 Continuity And Differentiability · Assertion Reason1 Marksassertion_reason

Class 12 Maths · Continuity And Differentiability · Assertion Reason #32

Assertion: For |x|<1, y=arcsin(2x/(1+x²)) satisfies y′=2/(1+x²). Reason: For |x|<1, arcsin(2x/(1+x²))=2arctan x, and (arctan x)′=1/(1+x²).

(A) Both A and R are true, and R correctly explains A.
(B) Both A and R are true, but R does not correctly explain A.
(C) A is true, but R is false.
(D) A is false, but R is true.

✅ Step-by-Step Solution

Final Answer: Option (A): Both A and R are true, and R correctly explains A.

Since 2arctan x lies in the arcsine principal interval when |x|<1, the stated identity is valid and differentiating it proves A.

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