For this problem, we want to split things up into sines and cosines for the tangent portion. So tangent is sine 5X over cosine 5X, and that's all still divided by sine 7X. Well, if we divide by sine 7X, we can really think of that as multiplying by one over sine 7X. So this is going to simplify into sine 5X over cosine 5X, sine 7X. Now to use the identity, the theorem that we developed, we need to split this up so that our sine terms currently have nothing with them. And if it's in the numerator, we need to leave it in the numerator. If it's in the denominator, we're going to leave it in the denominator. And then down here, I'm going to put whatever is left. So if there's a 5X sign, 5X on top, I need a 5X on bottom. If I put a 5X on bottom, I'm going to have to put a 5X on top to keep the equation balanced. If I have a sign of 7X on bottom, I need to put A7X on top, but if I put A7X on top, I have to put A7X on bottom. When I look at this, the limit as X goes to 0 of sine of 5X over 5X times the limit. As X goes to zero of seven X over sine 7X times the limit. As X goes to 0, the XS will cancel top and bottom here. So we're going to get 5 / 7, cosine 5X. So when we actually put X is zero, we get 1 * 1 * 5 / 7. What's the cosine of 0? Cosine of 0 is 1, so we get a final answer of 5 sevenths.