Question

Question #4e767

Answer 1

`tantheta(cottheta-costheta) = 1-sintheta`

Explanation:

I'm assuming the goal is to simplify this expression as much as possible.

Let's start by writing everything in terms of sine and cosine.

`tantheta(cottheta-costheta)`

`sintheta/costheta (costheta/sintheta - costheta)`

Now, distribute.

`(sinthetacostheta)/(costhetasintheta) - (sinthetacostheta)/costheta`

Finally, cancel everything out and simplify.

`(color(red)cancel(color(black)sintheta)color(blue)cancel(color(black)costheta))/(color(blue)cancel(color(black)costheta)color(red)cancel(color(black)sintheta)) - (sinthetacolor(blue)cancel(color(black)costheta))/color(blue)cancel(color(black)costheta)`

`1 - sintheta`

Final Answer