exercicio resolvido

por **adauto martins** » Qui Jun 24, 2021 17:12

(ITA-1959)mostre se é verdadeiro
para todo x tal que $(senx).(cosx)\neq 1/2$ , tem se

${tg}^{2}(x+\pi/4)=1/((1/2)-(senx)(cosx))$

por **adauto martins** » Qui Jun 24, 2021 17:24

soluçao

${tg}^{2}(x+\pi/4)+1={sec}^{2}(x+\pi/4)=1/({cos}^{2}(x+\pi/4)) =1/(cos(x+\pi/4))^2=1/((cosx.cos(\pi/4)-senx.sen(\pi/4))^2 =1/(cosx.(\sqrt[]{2})/2-senx.(\sqrt[]{2}/2))^2 =1/((\sqrt[]{2}/2))^2.(cosx-senx)^2=1/((1/2).(cos^2x-2cosx.senx+sen^2x)) =1/((1/2).(cos^2x+sen^2x-2.senx.cosx))=1/(1/2)(1-2senx.cosx)) =1/((1/2)-senx.cosx)...$

exercicio resolvido

exercicio resolvido

exercicio resolvido

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