00:05
To prove two trigonometric expressions are equivalent, we want to only work on one side of the equal sign and replace things with identities that we know to be true.
00:18
In this case, we know that cosine of the sum a plus b can be rewritten using the cosine sum identity.
00:26
So we can rewrite this as cosine a times cosine b minus sine a.
00:35
Times sine b over our common denominator of cosine a, cosine b.
00:44
Now, we want to break this into two separate fractions so that this will simplify.
00:50
So we're going to write this as cosine a times cosine b all over that denominator of cosine a times cosine b.
01:01
And i think you can see that has some promising simplification on the way.
01:06
Then we have our second term of the numerator, sine a times sine b, all over that common denominator of cosine a times cosine b...