{"id":225770,"date":"2025-06-04T15:12:57","date_gmt":"2025-06-04T15:12:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225770"},"modified":"2025-06-04T15:12:59","modified_gmt":"2025-06-04T15:12:59","slug":"when-ma-mb-90a-what-relationship-is-formed-by-tan-a-and-tan-b","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/when-ma-mb-90a-what-relationship-is-formed-by-tan-a-and-tan-b\/","title":{"rendered":"When mA + mB = 90\u00c2\u00b0, what relationship is formed by tan A and tan B"},"content":{"rendered":"\n

When mA + mB = 90\u00c2\u00b0, what relationship is formed by tan A and tan B? Select all that apply: (1 Point) 13.1 Tangent Ratio Problem – HOT Question tan A tan B tan A tan B = | tan\u00c2\u00b2 A tan\u00c2\u00b2 B = [ (tan A) (tan B) = 1 (tan A) (tan B) = -1<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Given that m\u2220A + m\u2220B = 90\u00b0<\/strong>, we are told that the angles A and B are complementary<\/strong>. This forms the basis of a fundamental trigonometric identity.<\/p>\n\n\n\n

\n\n\n\n

Correct Answer:<\/strong><\/h3>\n\n\n\n

(tan A)(tan B) = 1<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation<\/strong><\/h3>\n\n\n\n

When two angles are complementary, their measures add up to 90\u00b0. In this case, m\u2220A + m\u2220B = 90\u00b0<\/strong>, so we can write: \u2220B=90\u2218\u2212\u2220A\\angle B = 90^\\circ – \\angle A<\/p>\n\n\n\n

In trigonometry, the tangent<\/strong> of an angle in a right triangle is defined as: tan\u2061(\u03b8)=oppositeadjacent\\tan(\\theta) = \\frac{\\text{opposite}}{\\text{adjacent}}<\/p>\n\n\n\n

There\u2019s also a very important identity that relates the tangent of complementary angles: tan\u2061(A)=cot\u2061(B)if A+B=90\u2218\\tan(A) = \\cot(B) \\quad \\text{if } A + B = 90^\\circ<\/p>\n\n\n\n

But since: cot\u2061(B)=1tan\u2061(B),\\cot(B) = \\frac{1}{\\tan(B)},<\/p>\n\n\n\n

we get: tan\u2061(A)=1tan\u2061(B)\u21d2tan\u2061(A)\u22c5tan\u2061(B)=1\\tan(A) = \\frac{1}{\\tan(B)} \\Rightarrow \\tan(A) \\cdot \\tan(B) = 1<\/p>\n\n\n\n

This is the key relationship that holds when two angles are complementary<\/strong>.<\/p>\n\n\n\n

Let\u2019s test this with an example:<\/p>\n\n\n\n

    \n
  • Let A=30\u2218A = 30^\\circ \u2192 then B=60\u2218B = 60^\\circ<\/li>\n\n\n\n
  • tan\u2061(30\u2218)\u22480.577\\tan(30^\\circ) \\approx 0.577<\/li>\n\n\n\n
  • tan\u2061(60\u2218)\u22481.732\\tan(60^\\circ) \\approx 1.732<\/li>\n\n\n\n
  • Product: 0.577\u22c51.732\u224810.577 \\cdot 1.732 \\approx 1<\/li>\n<\/ul>\n\n\n\n

    This confirms the identity.<\/p>\n\n\n\n

    \n\n\n\n

    Why Other Options Are Incorrect:<\/strong><\/h3>\n\n\n\n
      \n
    • tan\u2061(A)+tan\u2061(B)\\tan(A) + \\tan(B): No specific identity relates this directly to complementary angles.<\/li>\n\n\n\n
    • tan\u20612(A)tan\u20612(B)\\tan^2(A) \\tan^2(B): This is the square of the correct identity, which equals 12=11^2 = 1, but it\u2019s not the basic or most direct relationship.<\/li>\n\n\n\n
    • (tan\u2061A)(tan\u2061B)=\u22121(\\tan A)(\\tan B) = -1: This is incorrect. That identity applies in perpendicular lines in coordinate geometry<\/strong>, not complementary angles.<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      Conclusion:<\/strong><\/h3>\n\n\n\n

      For two complementary angles, the product of their tangents is always 1<\/strong>. Thus, the correct relationship is: (tan\u2061A)(tan\u2061B)=1(\\tan A)(\\tan B) = 1<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      When mA + mB = 90\u00c2\u00b0, what relationship is formed by tan A and tan B? Select all that apply: (1 Point) 13.1 Tangent Ratio Problem – HOT Question tan A tan B tan A tan B = | tan\u00c2\u00b2 A tan\u00c2\u00b2 B = [ (tan A) (tan B) = 1 (tan A) (tan B) […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-225770","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225770","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=225770"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225770\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225770"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225770"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225770"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}