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sin-2-f-x-2-1-1-2-1-x-2-find-f-x-

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Question Number 141383 by Willson last updated on 18/May/21
sin^2 (((f(x))/2))=1−(1/2)(√(1−x^2 )) find f(x)
sin2(f(x)2)=1−121−x2findf(x)
Answered by mr W last updated on 18/May/21
sin^2 (((f(x))/2))=1−(1/2)(√(1−x^2 )) 1−sin^2 (((f(x))/2))=(1/2)(√(1−x^2 )) cos^2 (((f(x))/2))=(1/2)(√(1−x^2 )) 2cos^2 (((f(x))/2))−1=(√(1−x^2 ))−1 cos (f(x))=(√(1−x^2 ))−1 ⇒f(x)=cos^(−1) ((√(1−x^2 ))−1)
sin2(f(x)2)=1−121−x21−sin2(f(x)2)=121−x2cos2(f(x)2)=121−x22cos2(f(x)2)−1=1−x2−1cos(f(x))=1−x2−1⇒f(x)=cos−1(1−x2−1)

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