1.

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

Answer» `y=secx+tanx`
`=1/cosx+sinx/cosx=(1+sinx)/cosx` ,brgt `rArr(dy)/(dx)=d/(dx)((1+sinx)/cosx)`
`(cosxd/(dx)(1+sinx)-(1+sinx)d/(dx)cosx)/(cos^(2)x)`
`=(cosx.cosx+(1+sinx).sinx)/(cos^(2)x)`
`=(1+sinx)/(1-sin^2x)=1/(1-sinx)`
`rArr (d^(2)y)/(dx^2)=d/(dx)(1/(1-sinx))`
`=((1-sinx).d/(dx)(1)-1d/(dx)(1-sinx))/((1-sinx)^(2))`
`=(0+cosx)/((1-sinx)^(2))=cosx/((1-six)^(2))`


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