{"id":42823,"date":"2025-06-29T11:01:32","date_gmt":"2025-06-29T11:01:32","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=42823"},"modified":"2025-06-29T11:01:33","modified_gmt":"2025-06-29T11:01:33","slug":"how-do-you-simplify-csc-x-sin-x-cot-x","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/how-do-you-simplify-csc-x-sin-x-cot-x\/","title":{"rendered":"How do you simplify csc x sin x\/ cot x"},"content":{"rendered":"\n<p>How do you simplify csc x sin x\/ cot x<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To simplify the expression csc\u2061xsin\u2061xcot\u2061x\\frac{\\csc x \\sin x}{\\cot x}cotxcscxsinx\u200b, we can follow these steps:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Recall the Trigonometric Identities<\/h3>\n\n\n\n<p>First, we should recall the basic trigonometric identities:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>csc\u2061x=1sin\u2061x\\csc x = \\frac{1}{\\sin x}cscx=sinx1\u200b<\/li>\n\n\n\n<li>cot\u2061x=cos\u2061xsin\u2061x\\cot x = \\frac{\\cos x}{\\sin x}cotx=sinxcosx\u200b<\/li>\n<\/ul>\n\n\n\n<p>Now, we can rewrite the expression by substituting these identities: csc\u2061xsin\u2061xcot\u2061x=(1sin\u2061x)sin\u2061xcos\u2061xsin\u2061x\\frac{\\csc x \\sin x}{\\cot x} = \\frac{\\left(\\frac{1}{\\sin x}\\right) \\sin x}{\\frac{\\cos x}{\\sin x}}cotxcscxsinx\u200b=sinxcosx\u200b(sinx1\u200b)sinx\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Simplify the Numerator<\/h3>\n\n\n\n<p>In the numerator, we have 1sin\u2061x\u00d7sin\u2061x\\frac{1}{\\sin x} \\times \\sin xsinx1\u200b\u00d7sinx. The sin\u2061x\\sin xsinx terms cancel each other out, leaving us with: 11=1\\frac{1}{1} = 111\u200b=1<\/p>\n\n\n\n<p>So now the expression becomes: 1cos\u2061xsin\u2061x\\frac{1}{\\frac{\\cos x}{\\sin x}}sinxcosx\u200b1\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Simplify the Denominator<\/h3>\n\n\n\n<p>Now, simplify the fraction in the denominator. Dividing by cos\u2061xsin\u2061x\\frac{\\cos x}{\\sin x}sinxcosx\u200b is equivalent to multiplying by its reciprocal: 1cos\u2061xsin\u2061x=sin\u2061xcos\u2061x\\frac{1}{\\frac{\\cos x}{\\sin x}} = \\frac{\\sin x}{\\cos x}sinxcosx\u200b1\u200b=cosxsinx\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Final Simplification<\/h3>\n\n\n\n<p>Now, sin\u2061xcos\u2061x\\frac{\\sin x}{\\cos x}cosxsinx\u200b is just the definition of tan\u2061x\\tan xtanx: sin\u2061xcos\u2061x=tan\u2061x\\frac{\\sin x}{\\cos x} = \\tan xcosxsinx\u200b=tanx<\/p>\n\n\n\n<p>So, the simplified expression is: tan\u2061x\\tan xtanx<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>Therefore, the expression csc\u2061xsin\u2061xcot\u2061x\\frac{\\csc x \\sin x}{\\cot x}cotxcscxsinx\u200b simplifies to tan\u2061x\\tan xtanx. This process involved using basic trigonometric identities to eliminate terms and simplify the fraction step by step.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-384.jpeg\" alt=\"\" class=\"wp-image-42824\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-384.jpeg 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-384-300x300.jpeg 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-384-150x150.jpeg 150w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-384-768x768.jpeg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>How do you simplify csc x sin x\/ cot x The Correct Answer and Explanation is: To simplify the expression csc\u2061xsin\u2061xcot\u2061x\\frac{\\csc x \\sin x}{\\cot x}cotxcscxsinx\u200b, we can follow these steps: Step 1: Recall the Trigonometric Identities First, we should recall the basic trigonometric identities: Now, we can rewrite the expression by substituting these identities: csc\u2061xsin\u2061xcot\u2061x=(1sin\u2061x)sin\u2061xcos\u2061xsin\u2061x\\frac{\\csc [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-42823","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42823","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=42823"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42823\/revisions"}],"predecessor-version":[{"id":42825,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42823\/revisions\/42825"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=42823"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=42823"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=42823"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}