Question

Is this even odd or neither, and justify answer
f(x)= [x+sin(x)]/cos(x) Is this even odd or neither, and justify answer
f(x)= [x+sin(x)]/cos(x) @Mathematics

Answer 1

it is odd because
\[x+\sin(x)\] is odd and
\[\cos(x)\] is even

Answer 2

your teacher wants you to write
\[f(x)=\frac{x+\sin(x)}{\cos(x)}\]
\[f(-x)=\frac{-x+\sin(-x)}{\cos(-x)}=\frac{-x-\sin(x)}{\cos(x)}=-\frac{x+\sin(x)}{\cos(x)}=-f(x)\]

Answer 3

lol my teacher uses this stuff in calc 3 all the time and we think he just does it to show off

Answer 4

the second equal sign because
\[\sin(-x)=-\sin(x)\text{ and }\cos(-x)=\cos(x)\]

Answer 5

i guess it is useful for doing some integrals to know that the function is odd.
also will tell you what power series expansion contains only odd exponents