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Match the statements/expressions in List I statements/expression in List II |
Answer»  Given `2(a^(2) -B^(2)) = c^(2)` `RARR 2 (sin^(2) X - sin^(2)Y) = sin^(2)Z` `rArr 2 sin (X + Y) sin (X - Y) = sin^(2) Z` `rArr 2 sin (pi - Z) sin (X -Y) = sin^(2) Z` `rArr sin (X- Y) = (sin Z)/(2)`...(i) `:. lamda = (sin (X -Y))/(sin Z) = (1)/(2)` Now `cos (n pi lamda) = 0` `rArr cos ((n pi)/(2)) = 0` `:. n = 1, 3, 5`  `1 + cos 2X - 2 cos 2Y = 2 sin X sin Y` `2 cos^(2) X - 2 cos 2Y = 2 sin X sin Y` `1- sin^(2) X - 1 + 2 sin^(2) Y = sin X sin Y` `sin^(2) X + sin X sin Y = 2 sin^(2) Y` `sin X (sin X + sin Y) = 2 sin^(2) Y` `rArr a(a +b) = 2B^(2)` `rArr a^(2) + ab - 2b^(2) = 0` `rArr ((a)/(b))^(2) + (a)/(b) - 2 = 0` `rArr (a)/(b) = -2, 1` `rArr (a)/(b) = 1` Note : Solutions of the REMAINING parts are given in their respecitive chapters. |
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