\nSe [tex]sen(x) + cos(x) = m[\/tex], ent\u00e3o [tex]sen(2x)[\/tex] \u00e9 igual a:<\/p>\n
\n
Solu\u00e7\u00e3o<\/p>\n
\nSeja [tex]sen(x) + cos(x) = m[\/tex]; ent\u00e3o segue que:
\n[tex]\\qquad sen(x) + cos(x) = m \\\\
\n\\qquad(sen(x) + cos(x))^2 = m^2 \\\\
\n\\qquad sen^2(x) + 2 \\cdot sen(x) \\cdot cos(x)+cos^2(x) = m^2\\\\
\n\\qquad \\left(sen^2(x) + cos^2(x)\\right) + 2 \\cdot sen(x) \\cdot cos(x) = m^2\\,.[\/tex]
\nComo [tex]\\boxed{sen(2x) = 2 \\cdot sen(x) \\cdot cos(x)}\\;[\/tex] e [tex]\\;\\boxed{sen^2(x) + cos^2(x) = 1}[\/tex], segue, da \u00faltima igualdade, que
\n[tex]\\qquad 1 + sen(2x) = m^2[\/tex],
\ne, finalmente, conclu\u00edmos que
\n[tex]\\qquad \\fcolorbox{black}{#eee0e5}{$sen(2x) = m^2 – 1$}\\,[\/tex].<\/p>\n
\n
Solu\u00e7\u00e3o elaborada pelos Moderadores do Blog<\/strong>.<\/p>\n<\/div>\n\n
\nPrimeira Gincana de 2015 – Clubes de Matem\u00e1tica da OBMEP
\nN\u00edvel C – Quest\u00e3o F\u00e1cil<\/div>\n","protected":false},"excerpt":{"rendered":"
Problema Se [tex]sen(x) + cos(x) = m[\/tex], ent\u00e3o [tex]sen(2x)[\/tex] \u00e9 igual a: (A) [tex]2m[\/tex]. (B) [tex]m^2[\/tex]. (C) [tex]m^2 – 1[\/tex]. (D) [tex]m – 1[\/tex]. (E) [tex]m^2 – m[\/tex]. Solu\u00e7\u00e3o Seja [tex]sen(x) + cos(x) = m[\/tex]; ent\u00e3o segue que: [tex]\\qquad sen(x) + cos(x) = m \\\\ \\qquad(sen(x) + cos(x))^2 = m^2 \\\\ \\qquad sen^2(x) + 2 … <\/p>\n
Continue lendo<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-41679","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/41679","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=41679"}],"version-history":[{"count":18,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/41679\/revisions"}],"predecessor-version":[{"id":185147,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/41679\/revisions\/185147"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=41679"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}