00:01
For this problem, we need to verify this identity.
00:04
I'm going to start working with the left side.
00:07
And so the first thing i'm going to do is i'm going to square the first term.
00:11
Squaring, i get 1 minus 2, tangent x plus tangent square x.
00:21
And then if i square the second term, i'm going to have 1 minus 2, go -tangent x plus cotangent.
00:30
Square x next the 1 positive plus the tangent square x that's the same thing as sican square x and in the same way the 1 in the cotangent square x that's the same thing as co -sikin square x then what i have remaining is the negative 2 tangent x and the negative 2 co -tangent x.
01:04
Next, i'm going to concentrate on these two middle terms.
01:11
Now, i'm going to write tangent as sine x over cosine x, and then the co -tangent, i'm going to write it as cosine x over sine x.
01:26
Then i'm going to subtract these two fractions by making them the same denominator, so i'm going to multiply top and bottom of this one by sine x...