Question

доказать тождество:


(1+ tg)*(1+ctg) - 1/sin*cos=2

Answer 1

(1+tg)•(1+ctg) -1/(sin•cos)= (1+tg+ctg+tg•ctg) -1/(sin•cos)=
=(1+sin/cos+cos/sin+1) -1/(sin•cos)=
= 2+(sin²+cos²)/(sin•cos) -1/(sin•cos)=
= 2+1/(sin•cos) -1/(sin•cos)=2.