| sin(α - β) | sinαcosβ−cosαsinβ | Subtraction formula for sine - expands compound angles into basic functions |
| cos(α - β) | cosαcosβ+sinαsinβ | Subtraction formula for cosine - note the addition in the expansion |
| tan(α - β) | 1+tanαtanβtanα−tanβ | Subtraction formula for tangent - undefined when denominator equals zero |
| csc(α - β) | cscαcotβ−cotαcscβcscαcscβ | Reciprocal of sine difference - derived from basic subtraction formula |
| sec(α - β) | secαcotβ+tanαsecβsecαsecβ | Reciprocal of cosine difference - complex form for advanced calculations |
| cot(α - β) | cotβ−cotαcotαcotβ+1 | Subtraction formula for cotangent - derived from tangent difference formula |