00:01
We wish to show that the left -hand side of this equation is equal to the right -hand side.
00:06
So usually when you get something like this, you want to start with a more complicated side so that you can simplify that into the simpler -looking side.
00:14
So we're going to start on the left -hand side, and we're going to try to simplify that.
00:19
So there are multiple different ways of doing this, but what i'm going to do is instead of having tangent and sikant, i'm going to actually rewrite everything in terms of sine and cosine, just because those are the two easiest expressions to work with.
00:36
So 10theta, i'm going to say that since tan theta is sine theta or cosine data, i'm going to change that to that.
00:45
And then this is over 1 plus, and second data is 1 over cos theta.
00:54
So now do the same thing there.
00:56
This is 1 plus 1 over cosine beta all over this is sign beta over cosine theta so now we have fractions over fractions so we're going to actually simplify that so what i mean is the first one so this is sign theta over coast data so we'll leave our numerator but our denominator we're going to change that one to coast over coast so this is now going to be cosine data plus 1 over cosine theta.
01:32
The second one, we're going to do the same thing.
01:35
So the top, we have cosine theta plus one.
01:38
So we're changing this, this one to coast beta over coast theta, so we can put it over common denominator.
01:44
So now this is over cosine theta, and then on the bottom, we still have our sine theta over cosine theta.
01:53
So now we have a fraction over a fraction.
01:56
So that means we can just change it to multiplication and flip our denominator.
02:02
So this becomes sine theta over cosine theta.
02:08
And now it's multiplied by the reciprocal of the denominator.
02:12
So that's going to be cost data over coast data plus one.
02:18
And then the second one, same thing.
02:20
We can flip our denominator, change it to a multiplication.
02:24
So this becomes cost data over sine theta...