Question

Simplify completely: (tanx + cotx)/sec2x ?

Answer 1

This simplifies to `2cot(2x)`

Explanation:

We start by rewriting in sine and cosine.

`=(tanx + cotx)cos(2x)`

`=(sinx/cosx + cosx/sinx)cos2x`

`=((sin^2x + cos^2x)/(cosxsinx))(cos(2x))`

`= 1/(cosxsinx)*cos(2x)`

Recall that `sin(2x) = 2sinxcosx`.

`= 1/(1/2sin(2x)) * cos(2x)`

`=(2cos(2x))/sin(2x)`

`= 2cot(2x)`

Hopefully this helps!