To determine the exact value of tan\u2061(195\u2218)\\tan(195^\\circ)tan(195\u2218), we will use the difference formula<\/strong> for the tangent of angles, which is:tan\u2061(A\u2212B)=tan\u2061(A)\u2212tan\u2061(B)1+tan\u2061(A)\u22c5tan\u2061(B)\\tan(A – B) = \\frac{\\tan(A) – \\tan(B)}{1 + \\tan(A) \\cdot \\tan(B)}tan(A\u2212B)=1+tan(A)\u22c5tan(B)tan(A)\u2212tan(B)\u200b<\/p>\n\n\n\n We can express 195\u2218195^\\circ195\u2218 as 195\u2218=180\u2218+15\u2218195^\\circ = 180^\\circ + 15^\\circ195\u2218=180\u2218+15\u2218, so we will apply the difference formula with A=180\u2218A = 180^\\circA=180\u2218 and B=15\u2218B = 15^\\circB=15\u2218.<\/p>\n\n\n\n tan\u2061(195\u2218)=tan\u2061(180\u2218+15\u2218)\\tan(195^\\circ) = \\tan(180^\\circ + 15^\\circ)tan(195\u2218)=tan(180\u2218+15\u2218)<\/p>\n\n\n\n Using the difference formula for tangent:tan\u2061(195\u2218)=tan\u2061(180\u2218)\u2212tan\u2061(15\u2218)1+tan\u2061(180\u2218)\u22c5tan\u2061(15\u2218)\\tan(195^\\circ) = \\frac{\\tan(180^\\circ) – \\tan(15^\\circ)}{1 + \\tan(180^\\circ) \\cdot \\tan(15^\\circ)}tan(195\u2218)=1+tan(180\u2218)\u22c5tan(15\u2218)tan(180\u2218)\u2212tan(15\u2218)\u200b<\/p>\n\n\n\n From trigonometric identities, we know:tan\u2061(180\u2218)=0\\tan(180^\\circ) = 0tan(180\u2218)=0<\/p>\n\n\n\n Therefore, the equation simplifies to:tan\u2061(195\u2218)=0\u2212tan\u2061(15\u2218)1+0\u22c5tan\u2061(15\u2218)\\tan(195^\\circ) = \\frac{0 – \\tan(15^\\circ)}{1 + 0 \\cdot \\tan(15^\\circ)}tan(195\u2218)=1+0\u22c5tan(15\u2218)0\u2212tan(15\u2218)\u200b<\/p>\n\n\n\n This simplifies further to:tan\u2061(195\u2218)=\u2212tan\u2061(15\u2218)\\tan(195^\\circ) = -\\tan(15^\\circ)tan(195\u2218)=\u2212tan(15\u2218)<\/p>\n\n\n\n We can use the tangent subtraction formula for 15\u2218=45\u2218\u221230\u221815^\\circ = 45^\\circ – 30^\\circ15\u2218=45\u2218\u221230\u2218. The formula for the tangent of a difference is:tan\u2061(A\u2212B)=tan\u2061(A)\u2212tan\u2061(B)1+tan\u2061(A)\u22c5tan\u2061(B)\\tan(A – B) = \\frac{\\tan(A) – \\tan(B)}{1 + \\tan(A) \\cdot \\tan(B)}tan(A\u2212B)=1+tan(A)\u22c5tan(B)tan(A)\u2212tan(B)\u200b<\/p>\n\n\n\n Substitute A=45\u2218A = 45^\\circA=45\u2218 and B=30\u2218B = 30^\\circB=30\u2218:tan\u2061(15\u2218)=tan\u2061(45\u2218)\u2212tan\u2061(30\u2218)1+tan\u2061(45\u2218)\u22c5tan\u2061(30\u2218)\\tan(15^\\circ) = \\frac{\\tan(45^\\circ) – \\tan(30^\\circ)}{1 + \\tan(45^\\circ) \\cdot \\tan(30^\\circ)}tan(15\u2218)=1+tan(45\u2218)\u22c5tan(30\u2218)tan(45\u2218)\u2212tan(30\u2218)\u200b<\/p>\n\n\n\n Using known values for the tangents:tan\u2061(45\u2218)=1,tan\u2061(30\u2218)=13\\tan(45^\\circ) = 1, \\quad \\tan(30^\\circ) = \\frac{1}{\\sqrt{3}}tan(45\u2218)=1,tan(30\u2218)=3\u200b1\u200b<\/p>\n\n\n\n Substituting these values into the formula:tan\u2061(15\u2218)=1\u2212131+1\u22c513\\tan(15^\\circ) = \\frac{1 – \\frac{1}{\\sqrt{3}}}{1 + 1 \\cdot \\frac{1}{\\sqrt{3}}}tan(15\u2218)=1+1\u22c53\u200b1\u200b1\u22123\u200b1\u200b\u200b<\/p>\n\n\n\n Simplify the numerator and denominator:tan\u2061(15\u2218)=3\u2212133+13\\tan(15^\\circ) = \\frac{\\frac{\\sqrt{3} – 1}{\\sqrt{3}}}{\\frac{\\sqrt{3} + 1}{\\sqrt{3}}}tan(15\u2218)=3\u200b3\u200b+1\u200b3\u200b3\u200b\u22121\u200b\u200b<\/p>\n\n\n\n Canceling out 13\\frac{1}{\\sqrt{3}}3\u200b1\u200b:tan\u2061(15\u2218)=3\u221213+1\\tan(15^\\circ) = \\frac{\\sqrt{3} – 1}{\\sqrt{3} + 1}tan(15\u2218)=3\u200b+13\u200b\u22121\u200b<\/p>\n\n\n\n Since tan\u2061(195\u2218)=\u2212tan\u2061(15\u2218)\\tan(195^\\circ) = -\\tan(15^\\circ)tan(195\u2218)=\u2212tan(15\u2218), we get:tan\u2061(195\u2218)=\u22123\u221213+1\\tan(195^\\circ) = -\\frac{\\sqrt{3} – 1}{\\sqrt{3} + 1}tan(195\u2218)=\u22123\u200b+13\u200b\u22121\u200b<\/p>\n\n\n\n This is the exact value of tan\u2061(195\u2218)\\tan(195^\\circ)tan(195\u2218).<\/p>\n\n\n\n Use the sum or difference formula for tangent to determine the exact value of tan(195deg ). Make sure to simplify your answer. Use the sum or difference formula for tangent to determine the exact value of tan(195) Make sure to simplify your answer. The Correct Answer and Explanation is: To determine the exact value of […]<\/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-270259","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/270259","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=270259"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/270259\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=270259"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=270259"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=270259"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Apply the Difference Formula<\/h3>\n\n\n\n
Step 2: Simplify<\/h3>\n\n\n\n
Step 3: Find the Exact Value of tan\u2061(15\u2218)\\tan(15^\\circ)tan(15\u2218)<\/h3>\n\n\n\n
Step 4: Conclusion<\/h3>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1935.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"