if `y=tanx+secx` , prove that `(d^2y)/(dx^2)= cosx/((1-sinx)^2)`.

If y=(tan x+secx) , prove that (d^(2)y)/(dx^(2))=(cosx)/((1-sinx)^(2))

Solve: (d^2y)/dx^2=cosx-sinx

If y=5cosx-3sinx , prove that (d^2y)/(dx^2)+y=0 .

If y=2sinx+3cosx , prove that : y+(d^(2)y)/(dx^(2))=0

If y=5cosx-3sinx then prove that (d^2y)/(dx^2)+y=0

If y=5sinx-3sinx , prove that : (d^(2)y)/(dx^(2))+y=0 .

If y=e^tanx then prove that: cos^2x(d^2y)/(dx^2)-(1+sin2x)(dy)/dx=0

If y=(1-tanx)/(1+tanx) , prove that (dy)/(dx)=(-2)/(1+sin2x) .

If y=(sinx)^((sinx)^((sinx)...oo))," prove that "(dy)/(dx)=(y^(2)cotx)/((1-ylog sinx)).

"If "y=(x)^(cosx)+(sinx)^(tanx)", prove that "(dy)/(dx)=x^(cosx){(cosx)/(x)-(sinx)logx}+(sinx)^(tanx).{1+(log sinx)sec^(2)x}.