{"id":240613,"date":"2025-07-03T10:52:42","date_gmt":"2025-07-03T10:52:42","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=240613"},"modified":"2025-07-03T10:52:44","modified_gmt":"2025-07-03T10:52:44","slug":"identify-whether-the-following-equation-is-true-or-false","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/03\/identify-whether-the-following-equation-is-true-or-false\/","title":{"rendered":"Identify whether the following equation is true or false"},"content":{"rendered":"\n


Identify whether the following equation is true or false: sin x + sin y = sin (x+y) Choose the correct answer below: A. False, because sin x + sin y = sin (x + y) cos (x – y) and sin (x + y) = sin x cos y + cos x sin y B. True, because sin x + sin y = sin x cos y + cos x sin y which is equal to sin (x+y) C. True, because sin x + sin y = 2 sin x cos x which is equal to sin (x + y) D. False, because sin x + sin y = 2 sin x cos x and sin (x + y) = sin x cos y + cos x sin y<\/p>\n\n\n\n

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

The correct answer is D: False, because sin x + sin y = 2 sin x cos x and sin (x + y) = sin x cos y + cos x sin y.<\/strong><\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

The equation given is sin x + sin y = sin (x + y)<\/strong>, which is false. Let’s break it down:<\/p>\n\n\n\n

    \n
  1. The Left-Hand Side (sin x + sin y):<\/strong>
    The sum of the sines of two angles can be expressed using the sum-to-product identity<\/strong> in trigonometry: sin\u2061x+sin\u2061y=2sin\u2061(x+y2)cos\u2061(x\u2212y2)\\sin x + \\sin y = 2 \\sin\\left(\\frac{x + y}{2}\\right) \\cos\\left(\\frac{x – y}{2}\\right)sinx+siny=2sin(2x+y\u200b)cos(2x\u2212y\u200b) So, the sum of the sines is not simply equal to the sine of the sum of the angles. Instead, it involves both sine and cosine functions.<\/li>\n\n\n\n
  2. The Right-Hand Side (sin (x + y)):<\/strong>
    The formula for the sine of a sum of two angles is given by: sin\u2061(x+y)=sin\u2061xcos\u2061y+cos\u2061xsin\u2061y\\sin(x + y) = \\sin x \\cos y + \\cos x \\sin ysin(x+y)=sinxcosy+cosxsiny This is the sum formula<\/strong> for sine, which expresses the sine of a sum as the sum of products of sines and cosines.<\/li>\n<\/ol>\n\n\n\n

    Key Difference:<\/h3>\n\n\n\n
      \n
    • sin x + sin y<\/strong> is not equal<\/strong> to sin(x + y)<\/strong>.<\/li>\n\n\n\n
    • The identity for the sum of sines (as used on the left-hand side) involves both sine and cosine terms, while the identity for sin(x + y)<\/strong> involves products of sine and cosine of the individual angles.<\/li>\n<\/ul>\n\n\n\n

      Thus, the statement is false. The correct formula<\/strong> for sin(x + y)<\/strong> is sin x cos y + cos x sin y<\/strong>, which is very different from the sum of the two sines.<\/p>\n\n\n\n

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

      Identify whether the following equation is true or false: sin x + sin y = sin (x+y) Choose the correct answer below: A. False, because sin x + sin y = sin (x + y) cos (x – y) and sin (x + y) = sin x cos y + cos x sin y 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-240613","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240613","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=240613"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240613\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=240613"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=240613"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=240613"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}