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Determine: A = tg(x/2) + cotg (x/2) para sen x = 1/3?
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Verified answer
Primeiramente, lembre-se da seguinte identidade:
sen(x) = 2tg(x/2)/(1+tg²(x/2))
válida para todo x ≠ π+4kπ, k inteiro. Com ela em mente, encontramos:
A = tg(x/2)+cotg(x/2) = tg(x/2)+1/tg(x/2) = (tg²(x/2)+1)/tg(x/2) = 2/sen(x) = 6