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Answer» Givensin−1(x)+sin−1(1−x)=cos−1(x)sin−1(1−x)=cos−1(x)−sin−1(x)⇒(1−x)=sin[cos−1(x)−sin−1(x)]Usingsin−1(x)+cos−1(x)=π2So(1−x)=sin[π2−2sin−1(x)]=cos(2sin−1(x))=cos(cos−1(1−2x2))Using2sin−1(x)=cos−1(1−2x2)So(1−x)=(1−2x2)⇒2x2−x=0So2x2−x=0⇒x=0,x=12Now Put into Original Equation we get x=12 and x=0 satisfy the Given equation. |
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