Let f be the function defined by f(x)= (x+sinx)/(cosx) for -pi/2<x<pi/2 state whether f is an even or odd function. Determine f'(x) write an equation of the line tangent to the graph of f at the point where x=0

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Remember what even and odd functions mean.  Even: f(-x)=f(x). Odd: f(-x)=-f(x). Let's check it out:


Now, sin(-x) = -sin(x), but cos(-x)=cos(x), so we have

`=(-x-sin(x))/cos(x)=-(x+sin(x))/cos(x)` , which is -f(x).

This is the definition of an odd function.


(The entire section contains 171 words.)

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