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if x = a sec(theta) , y = b tan(theta) , prove that d2y/dx2= -(b^4/a^2y^3)

if x = a sec(theta) , y = b tan(theta) , prove that d2y/dx2= -(b^4/a^2y^3)

Grade:12

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
6 years ago
dx/d@=asec@tan@
dy/d@=bsec2@
dy/dx=bsec2@/asec@tan@
=b/a sec@/tan@
=b/acosec@
d2y/dx2= d/d@(dy/dx).d@/dx=d/d@(b/acosec@)d@/dx
=(-b/acosec@cot@)/asec@tan@=-b/atan3@ put tan@=y/b , we get
d2y/dx2=-b4/a2y3

Thanks & Regards
Rinkoo Gupta
AskIITians faculty

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