Question

How do you simplify `2tanxcos^2x`?

Answer 1

`2tan(x)cos^2(x) = sin(2x)`

Explanation:

`tan(x) = sin(x)/cos(x)`

So
`color(white)("XXX")2tan(x)cos^2(x)`

`color(white)("XXX") = 2sin(x)/cancel(cos(x))*cancel(cos(x))*cos(x)`

`color(white)("XXX") = 2sin(x)cos(x)`

which by the Double Angle Formula for Sines
`color(white)("XXX")=sin(2x)`