A : `sqrt(1-sin^(2)100^@) sec 100^(@) =-1`
R : ` sqrt(x^(2))=-x " if " x lt 0`

(sqrt(1-sin^(2)100^(@)))sec100^(@)=

Differentiate sin^(-1) ( 2 x sqrt( 1 - x^(2))) with respect to x if (1)/( sqrt(2)) lt x lt 1

Differentiate sin^(-1)(2x sqrt(1-x^(2))) with respect to sec^(-1)((1)/(sqrt(1-x^(2)))), if x in(0,1/sqrt(2))

Differentiate sin^(-1) ( 2 x sqrt( 1 - x^(2))) with respect to x if - (1)/( sqrt(2)) lt x lt (1)/( sqrt(2))

y = sec^(-1)((1)/(2x^(2) -1 )), 0 lt x lt (1)/(sqrt(2))