{"id":14133,"date":"2018-03-12T02:09:01","date_gmt":"2018-03-12T02:09:01","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14133"},"modified":"2022-01-11T10:46:04","modified_gmt":"2022-01-11T10:46:04","slug":"mostra-que","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14133","title":{"rendered":"Mostra que"},"content":{"rendered":"<p><ul id='GTTabs_ul_14133' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14133' class='GTTabs_curr'><a  id=\"14133_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14133' ><a  id=\"14133_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_14133'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Sendo\u00a0\u03b1 a amplitude de um \u00e2ngulo agudo, mostra que:<\/p>\n<p>\\[{\\left( {{\\mathop{\\rm sen}\\nolimits} \\alpha + \\cos \\alpha } \\right)^2} = 1 + 2{\\mathop{\\rm sen}\\nolimits} \\alpha \\times \\cos \\alpha \\]<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14133' onClick='GTTabs_show(1,14133)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14133'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Sendo\u00a0\u03b1 a amplitude de um \u00e2ngulo agudo, mostra que:<\/p>\n<p>\\[{\\left( {{\\mathop{\\rm sen}\\nolimits} \\alpha + \\cos \\alpha } \\right)^2} = 1 + 2{\\mathop{\\rm sen}\\nolimits} \\alpha \\times \\cos \\alpha \\]<\/p>\n<\/blockquote>\n<p>Com efeito, tem-se:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{{\\left( {{\\mathop{\\rm sen}\\nolimits} \\alpha + \\cos \\alpha } \\right)}^2}}&amp; = &amp;{{{{\\mathop{\\rm sen}\\nolimits} }^2}\\alpha + 2{\\mathop{\\rm sen}\\nolimits} \\alpha \\times \\cos \\alpha + {{\\cos }^2}\\alpha }\\\\{}&amp; = &amp;{\\underbrace {\\left( {{{{\\mathop{\\rm sen}\\nolimits} }^2}\\alpha + {{\\cos }^2}\\alpha } \\right)}_1 + 2{\\mathop{\\rm sen}\\nolimits} \\alpha \\times \\cos \\alpha }\\\\{}&amp; = &amp;{1 + 2{\\mathop{\\rm sen}\\nolimits} \\alpha \\times \\cos \\alpha }\\end{array}\\]<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14133' onClick='GTTabs_show(0,14133)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sendo\u00a0\u03b1 a amplitude de um \u00e2ngulo agudo, mostra que: \\[{\\left( {{\\mathop{\\rm sen}\\nolimits} \\alpha + \\cos \\alpha } \\right)^2} = 1 + 2{\\mathop{\\rm sen}\\nolimits} \\alpha \\times \\cos \\alpha \\] Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14062,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[426,491,490],"series":[],"class_list":["post-14133","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-trigonometria-9--ano","tag-9-o-ano","tag-cosseno","tag-seno"],"views":2074,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat07.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14133","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=14133"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14133\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14062"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14133"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14133"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14133"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14133"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}