Verify that the trigonometric equation is an identity. 1+ secx 1-secx 1- secx 1+ secx -=-4 cot\u00c3\u201a\u00c2\u00b2x secx Which of the following statements establishes the identity? OA. 1+ secx 1-secx (1+ secx)\u00c3\u201a\u00c2\u00b2-(1-secx)\u00c3\u201a\u00c2\u00b24 secx 1-secx 1+ secx (1-secx)(1+ secx) 1-sec\u00c3\u201a\u00c2\u00b2x OB. 1+ secx 1-secx (1+cscx-(1-cscx 1-secx 1 secx (1-cscx)(1+cscx) OC. 1+ secx 1-secx 1- secx 1+ secx OD. 1+ secx 1-secx 1-secx 1+ secx 4cscx 1-csC\u00c3\u201a\u00c2\u00b2x (sinx+1)-(sinx-1) 4 sinx (sinx-1)(sinx+1) \u00c3\u201a\u00c2\u00b2x-1 (cosx+1-(cosx-12 4cosx (cosx-1)(cosx+1) cos\u00c3\u201a\u00c2\u00b2x-1 4 secx tan x 4cScx cotx -=-4 cotx secx 4 sin x<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The given trigonometric equation to verify as an identity is:<\/p>\n\n\n\n [ We are tasked with verifying this and determining which of the provided steps establishes the identity.<\/p>\n\n\n\n The left-hand side (LHS) is:<\/p>\n\n\n\n [ Observe that multiplying these two fractions simplifies as:<\/p>\n\n\n\n [ Thus, the LHS simplifies to 1<\/strong>.<\/p>\n\n\n\n The right-hand side (RHS) is:<\/p>\n\n\n\n [ For the equation to be an identity, the LHS must equal the RHS. However, the LHS simplifies to 1<\/strong>, while the RHS simplifies to a trigonometric expression involving (\\cot^2 x) and (\\sec x). Clearly, these two sides are not equal for all (x). This means the given equation is not an identity<\/strong>.<\/p>\n\n\n\n None of the provided options establish the given equation as an identity because the equation itself is incorrect. The simplified LHS and RHS are not equal, and the equation fails to hold universally.<\/p>\n","protected":false},"excerpt":{"rendered":" Verify that the trigonometric equation is an identity. 1+ secx 1-secx 1- secx 1+ secx -=-4 cot\u00c3\u201a\u00c2\u00b2x secx Which of the following statements establishes the identity? OA. 1+ secx 1-secx (1+ secx)\u00c3\u201a\u00c2\u00b2-(1-secx)\u00c3\u201a\u00c2\u00b24 secx 1-secx 1+ secx (1-secx)(1+ secx) 1-sec\u00c3\u201a\u00c2\u00b2x OB. 1+ secx 1-secx (1+cscx-(1-cscx 1-secx 1 secx (1-cscx)(1+cscx) OC. 1+ secx 1-secx 1- secx 1+ […]<\/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-185368","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185368","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=185368"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185368\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=185368"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=185368"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=185368"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\frac{1 + \\sec x}{1 – \\sec x} \\cdot \\frac{1 – \\sec x}{1 + \\sec x} = -4 \\cot^2 x \\sec x
]<\/p>\n\n\n\n
\n\n\n\nStep 1: Simplify the left-hand side<\/h3>\n\n\n\n
\\frac{1 + \\sec x}{1 – \\sec x} \\cdot \\frac{1 – \\sec x}{1 + \\sec x}
]<\/p>\n\n\n\n
\\frac{1 + \\sec x}{1 – \\sec x} \\cdot \\frac{1 – \\sec x}{1 + \\sec x} = 1
]<\/p>\n\n\n\n
\n\n\n\nStep 2: Examine the right-hand side<\/h3>\n\n\n\n
-4 \\cot^2 x \\sec x
]<\/p>\n\n\n\nStep 3: Compare LHS and RHS<\/h3>\n\n\n\n
\n\n\n\nCorrect Answer<\/h3>\n\n\n\n