If `sin^(-1)(1-x)-2 sin^(-1)x=(pi)/(2)`, then `x` is equal toA. `0,(1)/(2)`B. `1,(1)/(2)`C. `0`D. `(1)/(2)`

If `sin^(-1)(1-x)-2 sin^(-1)x=(pi)/(2)`, then `x` is equal toA. `0,(1)

1.	If `sin^(-1)(1-x)-2 sin^(-1)x=(pi)/(2)`, then `x` is equal toA. `0,(1)/(2)`B. `1,(1)/(2)`C. `0`D. `(1)/(2)`
Answer» Correct Answer - C `sin^(-1)(1-x)-2sin^(-1)x=(pi)/(2)" " Let sin^(-1)x=theta` `" "implies x=sintheta` `implies sin^(-1)(1-sintheta)-2theta=(pi)/(2)` `impliessin^(-1)(1-sin theta)=((pi)/(2)+2 theta)` `1-sin theta=sin((pi)/(2)+2theta)` `= cos 2 theta=1-sin^(2)theta` `implies 2sin^(2) theta -sin theta =0 implies 2x^(2)-x=0` `implies x(2x-1)=0 impliesx=0 or x=(1)/(2)` but the given equation is not satisfied by x`=(1)/(2)` `: . x=0`

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