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Principle Of Mathematical Induction

Question

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In $increment ABC comma$ if $fraction numerator sin space straight A over denominator sin space straight C end fraction equals space fraction numerator sin space left parenthesis straight A minus straight B right parenthesis over denominator sin space left parenthesis straight B minus straight C right parenthesis end fraction comma$ show that $straight a squared comma space straight b squared comma space straight c squared$ are in A.P.

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If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

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