ctg38×ctg22-1/ctg38+ctg22

[tex]ctg( \alpha + \beta )= \dfrac{ctg \alpha \cdot ctg \beta -1}{ctg \beta +ctg \alpha } [/tex]

В нашем случае:

[tex] \dfrac{ctg38а\cdot ctg22а-1}{ctg38а+ctg22а} =ctg(38а+22а)=ctg60а= \dfrac{1}{\sqrt{3}} [/tex]