To find the exact value of tan\u2061\u22121(3)\\tan^{-1}(\\sqrt{3})tan\u22121(3\u200b), we need to recognize that this represents the angle \u03b8\\theta\u03b8 whose tangent is equal to 3\\sqrt{3}3\u200b. In other words, we are solving for \u03b8\\theta\u03b8 in the equation:tan\u2061(\u03b8)=3\\tan(\\theta) = \\sqrt{3}tan(\u03b8)=3\u200b<\/p>\n\n\n\n
Now, let’s recall the standard values of the tangent function for common angles. We know that:tan\u2061(\u03c03)=3\\tan\\left(\\frac{\\pi}{3}\\right) = \\sqrt{3}tan(3\u03c0\u200b)=3\u200b<\/p>\n\n\n\n
This tells us that the angle \u03b8\\theta\u03b8 whose tangent is 3\\sqrt{3}3\u200b is \u03c03\\frac{\\pi}{3}3\u03c0\u200b radians.<\/p>\n\n\n\n
Thus, the exact value of tan\u2061\u22121(3)\\tan^{-1}(\\sqrt{3})tan\u22121(3\u200b) is:tan\u2061\u22121(3)=\u03c03\\tan^{-1}(\\sqrt{3}) = \\frac{\\pi}{3}tan\u22121(3\u200b)=3\u03c0\u200b<\/p>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
The inverse tangent function, tan\u2061\u22121(x)\\tan^{-1}(x)tan\u22121(x), gives us the angle \u03b8\\theta\u03b8 such that tan\u2061(\u03b8)=x\\tan(\\theta) = xtan(\u03b8)=x. In this case, we are asked to find tan\u2061\u22121(3)\\tan^{-1}(\\sqrt{3})tan\u22121(3\u200b), meaning we are looking for the angle whose tangent is 3\\sqrt{3}3\u200b. By recognizing the standard angle where the tangent function equals 3\\sqrt{3}3\u200b, we can quickly identify that \u03c03\\frac{\\pi}{3}3\u03c0\u200b is the correct angle.<\/p>\n\n\n\n
In radians, \u03c03\\frac{\\pi}{3}3\u03c0\u200b is equivalent to 60 degrees, so we could also express the solution as:tan\u2061\u22121(3)=60\u2218\\tan^{-1}(\\sqrt{3}) = 60^\\circtan\u22121(3\u200b)=60\u2218<\/p>\n\n\n\n
However, in most mathematical contexts, the answer is typically left in radians, so the exact value is \u03c03\\frac{\\pi}{3}3\u03c0\u200b radians.<\/p>\n\n\n\n Find the exact value of the following expression. tan ^-1 Square root of 3 The Correct Answer and Explanation is: To find the exact value of tan\u2061\u22121(3)\\tan^{-1}(\\sqrt{3})tan\u22121(3\u200b), we need to recognize that this represents the angle \u03b8\\theta\u03b8 whose tangent is equal to 3\\sqrt{3}3\u200b. In other words, we are solving for \u03b8\\theta\u03b8 in the equation:tan\u2061(\u03b8)=3\\tan(\\theta) = […]<\/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-253010","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253010","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=253010"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/253010\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=253010"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=253010"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=253010"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-318.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"