Sum and Difference formula in relation to the half angle formula

 The first picture depicts using the half angle formula to find the sine,cosine,and tangent for the angle 105 degrees. The second picture shows using the sum formula to find sine,cosine, and tangent for the same angle. When using the half angle formula, you need to pay attention to what is positive and negative based on the quadrant that your half angle is in. When we solve with the half angle formula and the sum formula we find that our answers are the same for sine, cosine, and tangent. Our answers are written differently when we solve using both formulas, however they are equivalent. We can check by plugging in our answers for sine,cosine,and tangent for both formulas in our calculator , and we find that our answers are the same. The two pictures above depict how to plug our answers into our calculator and shows that they are the same.