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irisha21
@irisha21
July 2022
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доказать тождество:
(1+ tg)*(1+ctg) - 1/sin*cos=2
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KoJl6a
(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.
3 votes
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Answers & Comments
=(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.