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If `sin^(-1)x+sin^(-1)y=(2pi)/3` and `cos^(-1)x-cos^(-1)y=-pi/3` then the number of values of `(x,y)` is |
Answer» Correct Answer - `x = (1)/(2), y = 1` Given equation are `sin^(-1) x + sin^(-1) y = (2pi)/(3)` `cos^(-1) x - cos^(-1) y = (pi)/(3)` `rArr ((pi)/(2) - sin^(-1) x) - ((pi)/(2) - sin^(-1) y) = (pi)/(3)` Let `sin^(-1) x = A` `sin^(-1) y = B` Then Eqs. (i) and (ii) become `A + B = (2pi)/(3)` `A - B = -(pi)/(3)` Solving Eqs. (iii) and (iv), we get `A = (pi)/(6), B = (pi)/(2)` `rArr sin^(-1) x = (pi)/(6), sin^(-1) y = (pi)/(2)` `rArr x = (1)/(2) and y = 1` |
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