Determine whether the following functionfx74sinxcosx is even

Determine whether the following functionf(x)=(7/4)sin(x)cos(x) is even, odd or neither. Show your work.

Solution

f(x)=(7/4)sin(x)cos(x)

f(-x)=(7/4)sin(-x)cos(-x)

f(-x)=(7/4)(-sin(x))(cos(x))

f(-x)=-(7/4)sin(x)cos(x)

f(-x)=-f(x)

Therefore, f(x) is odd function.