st","extracted_subject":"MATH","extracted_chapter":"INVERSE TRIGONOMETRIC FUNCTIONS","extracted_topic":"PRINCIPAL & GENERAL VALUE OF I.T.F","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2107.png?top_left_x=0&top_left_y=1740&width=532&height=265&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e73425d76b7ab3203b4","slug":"if-a-left---frac3pi2---pi-right-then-the-value-of-","content":"If a Î\\(\\left( - \\frac{3\\pi}{2}, - \\pi \\right)\\), then the value of\n\ntan^–1(cot a) – cot^–1(tan a) + sin^–1(sin a) + cos^–1(cosa) is equal to-","options":[{"_id":"68aad22e7f15af4716dda912","text":"2p + a","sequence":0,"isCorrect":false},{"_id":"68aad22e7f15af4716dda913","text":"p + a","sequence":1,"isCorrect":false},{"_id":"68aad22e7f15af4716dda914","text":"0","sequence":2,"isCorrect":true},{"_id":"68aad22e7f15af4716dda915","text":"p – a","sequence":3,"isCorrect":false}],"correct_answer":"0","explanation":"For a Î \\(\\left( - \\frac{3\\pi}{2}, - \\pi \\right)\\), tan a \\< 0\n\ñ tan^–1(cot a) – cot^–1(tan a) = – p\n\nAlso for points in 2^nd quadrant\n\nsin^–1(sin a) + cos^–1(cos a) = p.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:39.579Z","__v":0,"vector_store_id":"62da2d97-95e2-447d-964f-a26de311333e","updated_at":"2024-08-30T21:49:39.579Z","isStarred":false},"params":{"questionSlug":"if-a-left---frac3pi2---pi-right-then-the-value-of-"}}]}]]

Question: If a Î\(\left( - \frac{3\pi}{2}, - \pi \right)\), then the value of tan<sup>–1</sup>(cot a) – cot<s...

Solution