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If `x=asint `and `y=a(cost+logtant/2)`, find `(d^2 y)/(dx^2)` |
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Answer» `x = asint` `=>dx/dt = acost` `y = a(cost+logtan(t/2))` `=>dy/dt = a(-sint+1/tan(t/2)(1/2sec^2(t/2)))` `=>dy/dt = a(-sint + 1/(2sin (t/2)cos (t/2)))` `=>dy/dt = a(-sint + 1/sint)` `=>dy/dt = a((1-sin^2t)/sint)` `=>dy/dt = a(cos^2t/sint)` `=>dy/dt = a(costcot t)` `=>dy/dx = dy/dt*dt/dx = (acostcott)/(acost )= cott` `=>(d^2y)/dx^2 = -cosec^2 t*dt/dx` `=>(d^2y)/dx^2 = -cosec^2 t*(1/(acost))` `=>(d^2y)/dx^2 = -1/acosec^2tsect` |
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