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If `x = sqrt(a^(sin^(-1)t)) , y = sqrt(a^(cos^(-1)t)` then show that,`dy/dx=-y/x.`A. `(-y)/x`B. `x/y`C. `y/x`D. `(-x)/y` |
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Answer» Correct Answer - A We have , `x = sqrt(a^(sin t)), y = sqrt(a^(cos-1)t)` `therefore " " xy = sqrt(a^(sin-1t) . a^(cos-1t)) = sqrt(a^(sint+cos^(-1)t))` `rArr xy = sqrt(a^(pi//2))" "(because sin^(-1) t+ cos^(-1) =(pi)/(2))` On differentiating both sides w.r.t .x., we get `x(dy)/(dx) + y =0` `rArr " "(dy)/(dx) = (-y)/(x)` |
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