" 143) Hrof "cos^(-1)x=2sin^(-1)(1-x)/(2)

Statement -1: if -1lexle1 then sin^(-1)(-x)=-sin^(-1)x and cos^(-1)(-x)=pi-cos^(-1)x Statement-2: If -1lexlex then cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))= 2cos^(-1)sqrt((1+x)/(2))

Statement -1: if -1lexle1 then sin^(-1)(-x)=-sin^(-1)x and cos^(-1)(-x)=pi-cos^(-1)x Statement-2: If -1lexlex then cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))= 2cos^(-1)sqrt((1+x)/(2))

prove that cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))=2cos^(-1)sqrt((1+x)/(2))

cos^(-1)(1-2sin^(2)x)

cos(2sin^(-1)x)=1-2x^(2)

Prove the followings : cos^(-1)x=2sin^(-1)sqrt((1-x)/2)=2cos^(-1)sqrt((1+x)/2)

" (2) "sin^(-1)x+sin^(-1)(1/x)+cos^(-1)x+cos^(-1)(1/x)" is equal to "

sin^(-1)(2cos^(2)x-1)

sin^(2)(cos^(-1)x)+cos^(2)(sin^(-1)(sqrt(1-x^(2)))) = ________ (0ltxlt1)

prove that , sin ^(-1) cos sin ^(-1 )x+cos ^(-1) sin cos ^(-1) ""x=(pi)/(2)