Question #4e767

1 Answer
John D.
May 30, 2017

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

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