st","extracted_subject":"MATH","extracted_chapter":"FUCTIONS, LIMITS, CONTINIUITY AND DIFFTERENTIABILITY","extracted_topic":"FUNCTIONS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1595.png?top_left_x=0&top_left_y=1250&width=532&height=243&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e6f425d76b7ab31bf03","slug":"if-cossup-1supx-cotsup-1supx-0-where-denotes-the-g","content":"If [cos^-1x] + [cot^-1x] = 0, where [.] denotes the greatest integer function, then complete set of values of x is","options":[{"_id":"68a382e47f15af4716b74c9f","text":"(cos 1,1\\]","sequence":0,"isCorrect":false},{"_id":"68a382e47f15af4716b74ca0","text":"(cos 1, cot 1)","sequence":1,"isCorrect":false},{"_id":"68a382e47f15af4716b74ca1","text":"(cot 1, 1\\]","sequence":2,"isCorrect":true},{"_id":"68a382e47f15af4716b74ca2","text":"\\[0, cot 1)","sequence":3,"isCorrect":false}],"correct_answer":"(cot 1, 1\\]","explanation":"We have [cos⁻¹ x] ≥ 0 ∀ x ∈ [-1, 1]\n\nand [cos^-1x] ≥ 0 ∀ x ∈ R\n\n⇒ [cos⁻¹x] + [cot^-1x] = 0\n\n⇒ [cos^-1x] = [cot^-1x] = 0 If [cos^-1x] = 0\n\n⇒ x ∈ (cos 1, 1\\]\n\nIf [cot^-1x] = 0\n\n⇒ x ∈ (cot^-1x, ∞)\n\n⇒ x ∈ (cot 1, 1\\]","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:35.148Z","__v":0,"vector_store_id":"09e69b05-4f48-4f82-9b3c-37448c51ec88","updated_at":"2024-08-30T21:49:35.148Z","isStarred":false},"params":{"questionSlug":"if-cossup-1supx-cotsup-1supx-0-where-denotes-the-g"}}]}]]

Question: If [cos<sup>-1</sup>x] + [cot<sup>-1</sup>x] = 0, where [.] denotes the greatest integer function, t...

Solution