Evaluate the following limits: `lim_(xrarr0)((e^(tan-x)-1))/(tanx)`

1.	Evaluate the following limits: `lim_(xrarr0)((e^(tan-x)-1))/(tanx)`
Answer» Correct Answer - `(2a sin a+a^(2)cosa)` Given limit `=lim_(hto0)((a^(2)+h^(2)+2ah)sin(a+h)-a^(2)sina)/(h)` `=a^(2).lim_(hto0)(sin(a+h)-sina)/(h)+lim_(hto0)h sin(a+h)+lim_(hto0)2a sin(a+h)` `=a^(2). lim_(hto0)(cos(a+(h)/(2)).sin((h)/(2)))/((h//2))+0+2asina` `=a^(2).lim_(xto0)cos(a+(h)/(2)). lim_(hto0)(sin(h//2))/((h//2))+2asina` `=(a^(2)xxcosaxx1)+2asina=(a^(2)cosa+2asina).`

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