Dear Aditi,

Expand tan x using taylors theorem and then reduce the expression to get the answer.

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the Mcclaurin series expansion is

e^y=∑_{y=0 to ∞}yⁿ/n!

therefore, lim x→0   (e^tanx -  e^x) / (tan x -x)=1+(1/(tanx-x))(tan²x-x²+tan³x-x³...

=1+(1/(tanx-x))(tan²x/(1-tanx))-(x²/(1-x))=1+tanx+x=1

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Dear Aditi

take e^x   as common

so we get

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