{"id":14219,"date":"2018-03-31T00:52:06","date_gmt":"2018-03-30T23:52:06","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14219"},"modified":"2022-01-11T11:48:13","modified_gmt":"2022-01-11T11:48:13","slug":"mostra-que-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14219","title":{"rendered":"Mostra que"},"content":{"rendered":"<p><ul id='GTTabs_ul_14219' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14219' class='GTTabs_curr'><a  id=\"14219_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14219' ><a  id=\"14219_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_14219'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Mostra que:<\/p>\n<ol>\n<li>\\(2{{\\mathop{\\rm sen}\\nolimits} ^2}\\alpha &#8211; 1 = \\left( {{\\mathop{\\rm sen}\\nolimits} \\alpha &#8211; \\cos \\alpha } \\right)\\left( {{\\mathop{\\rm sen}\\nolimits} \\alpha + \\cos \\alpha } \\right)\\)<\/li>\n<li>\\(1 + \\frac{1}{{{{{\\mathop{\\rm tg}\\nolimits} }^2}\\theta }} = \\frac{1}{{{{{\\mathop{\\rm sen}\\nolimits} }^2}\\theta }}\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14219' onClick='GTTabs_show(1,14219)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14219'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Tendo em considera\u00e7\u00e3o a F\u00f3rmula Fundamental da Trigonometria e o caso not\u00e1vel &#8220;diferen\u00e7a de dois quadrados&#8221;, temos:<br \/>\n\\[\\begin{array}{*{20}{l}}{2{{{\\mathop{\\rm sen}\\nolimits} }^2}\\alpha &#8211; 1}&amp; = &amp;{2{{{\\mathop{\\rm sen}\\nolimits} }^2}\\alpha &#8211; \\left( {{{{\\mathop{\\rm sen}\\nolimits} }^2}\\alpha + {{\\cos }^2}\\alpha } \\right)}\\\\{}&amp; = &amp;{2{{{\\mathop{\\rm sen}\\nolimits} }^2}\\alpha &#8211; {{{\\mathop{\\rm sen}\\nolimits} }^2}\\alpha &#8211; {{\\cos }^2}\\alpha }\\\\{}&amp; = &amp;{{{{\\mathop{\\rm sen}\\nolimits} }^2}\\alpha &#8211; {{\\cos }^2}\\alpha }\\\\{}&amp; = &amp;{\\left( {{\\mathop{\\rm sen}\\nolimits} \\alpha &#8211; \\cos \\alpha } \\right)\\left( {{\\mathop{\\rm sen}\\nolimits} \\alpha + \\cos \\alpha } \\right)}\\end{array}\\]<br \/>\n\u00ad<\/li>\n<li>Tendo em considera\u00e7\u00e3o \\({\\mathop{\\rm tg}\\nolimits} \\alpha = \\frac{{{\\mathop{\\rm sen}\\nolimits} \\alpha }}{{\\cos \\alpha }}\\) e a Formula Fundamental da Trigonometria, vem:<br \/>\n\\[\\begin{array}{*{20}{l}}{1 + \\frac{1}{{{{{\\mathop{\\rm tg}\\nolimits} }^2}\\theta }}}&amp; = &amp;{1 + \\frac{1}{{\\frac{{{{{\\mathop{\\rm sen}\\nolimits} }^2}\\theta }}{{{{\\cos }^2}\\theta }}}}}\\\\{}&amp; = &amp;{1 + \\frac{{{{\\cos }^2}\\theta }}{{{{{\\mathop{\\rm sen}\\nolimits} }^2}\\theta }}}\\\\{}&amp; = &amp;{\\frac{{{{{\\mathop{\\rm sen}\\nolimits} }^2}\\theta }}{{{{{\\mathop{\\rm sen}\\nolimits} }^2}\\theta }} + \\frac{{{{\\cos }^2}\\theta }}{{{{{\\mathop{\\rm sen}\\nolimits} }^2}\\theta }}}\\\\{}&amp; = &amp;{\\frac{{{{{\\mathop{\\rm sen}\\nolimits} }^2}\\theta + {{\\cos }^2}\\theta }}{{{{{\\mathop{\\rm sen}\\nolimits} }^2}\\theta }}}\\\\{}&amp; = &amp;{\\frac{1}{{{{{\\mathop{\\rm sen}\\nolimits} }^2}\\theta }}}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14219' onClick='GTTabs_show(0,14219)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Mostra que: \\(2{{\\mathop{\\rm sen}\\nolimits} ^2}\\alpha &#8211; 1 = \\left( {{\\mathop{\\rm sen}\\nolimits} \\alpha &#8211; \\cos \\alpha } \\right)\\left( {{\\mathop{\\rm sen}\\nolimits} \\alpha + \\cos \\alpha } \\right)\\) \\(1 + \\frac{1}{{{{{\\mathop{\\rm tg}\\nolimits} }^2}\\theta }}&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14057,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[426,491,490,492],"series":[],"class_list":["post-14219","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","tag-tangente"],"views":2846,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat02.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14219","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=14219"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14219\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14057"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14219"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14219"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14219"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}