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[br]\arcsin{x}=\arccos{x}[br]\\[br]x=\sin\left ( \arccos{x} \right )[br]\\[br]x=\sqrt{1-\left ( \cos\left ( \arccos{x} \right ) \right )^2} \because \sin^2 \theta+\cos^2 \theta =1 \Rightarrow \sin \theta=\sqrt{1-\cos^2 \theta}[br]\\x=\sqrt{1-x^2}[br]x^2=1-x^2[br]\\[br]2x^2=1[br]\\[br]x^2=\frac{1}{2}[br]\\[br]x=\sqrt{\frac{1}{2}}[br]\\[br]\therefore x=\frac{\sqrt{2}}{2} \because \text{rationalise denominator}[br]
[br]\arcsin{x}=\arccos{x}[br]\\[br]x=\sin\left ( \arccos{x} \right )[br]\\[br]x=\sqrt{1-\left ( \cos\left ( \arccos{x} \right ) \right )^2} \because \sin^2 \theta+\cos^2 \theta =1 \Rightarrow \sin \theta=\sqrt{1-\cos^2 \theta}[br]\\x=\sqrt{1-x^2}[br]x^2=1-x^2[br]\\[br]2x^2=1[br]\\[br]x^2=\frac{1}{2}[br]\\[br]x=\sqrt{\frac{1}{2}}[br]\\[br]\therefore x=\frac{\sqrt{2}}{2} \because \text{rationalise denominator}[br]