{"id":50963,"date":"2021-05-24T17:56:00","date_gmt":"2021-05-24T12:26:00","guid":{"rendered":"https:\/\/samacheerkalviguru.com\/?p=50963"},"modified":"2021-05-24T17:56:00","modified_gmt":"2021-05-24T12:26:00","slug":"samacheer-kalvi-12th-maths-guide-chapter-4-ex-4-1-in-tamil","status":"publish","type":"post","link":"https:\/\/samacheerkalviguru.com\/samacheer-kalvi-12th-maths-guide-chapter-4-ex-4-1-in-tamil\/","title":{"rendered":"Samacheer Kalvi 12th Maths Guide Chapter 4 \u0ba8\u0bc7\u0bb0\u0bcd\u0bae\u0bbe\u0bb1\u0bc1 \u0bae\u0bc1\u0b95\u0bcd\u0b95\u0bcb\u0ba3\u0bb5\u0bbf\u0baf\u0bb2\u0bcd \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bcd Ex 4.1"},"content":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 12th Maths Guide<\/a> Pdf Chapter 4 \u0ba8\u0bc7\u0bb0\u0bcd\u0bae\u0bbe\u0bb1\u0bc1 \u0bae\u0bc1\u0b95\u0bcd\u0b95\u0bcb\u0ba3\u0bb5\u0bbf\u0baf\u0bb2\u0bcd \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bcd Ex 4.1 Textbook Questions and Answers, Notes.<\/p>\n

TN Board 12th Maths Solutions Chapter 4 \u0ba8\u0bc7\u0bb0\u0bcd\u0bae\u0bbe\u0bb1\u0bc1 \u0bae\u0bc1\u0b95\u0bcd\u0b95\u0bcb\u0ba3\u0bb5\u0bbf\u0baf\u0bb2\u0bcd \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bcd Ex 4.1<\/h2>\n

Question 1.
\nx-\u0ba9\u0bcd \u0b85\u0ba9\u0bc8\u0ba4\u0bcd\u0ba4\u0bc1 \u0bae\u0ba4\u0bbf\u0baa\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bc8\u0baf\u0bc1\u0bae\u0bcd \u0b95\u0bbe\u0ba3\u0bcd\u0b95.
\n(i) -10\u03c0 \u2264 x \u2264 10\u03c0 \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd sin x = 0
\n(ii) -8\u03c0 \u2264 x \u2264 8\u03c0 and sin x = -1.
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1:
\n(i) \u0b95\u0bca\u0b9f\u0bc1\u0b95\u0bcd\u0b95\u0baa\u0bcd\u0baa\u0b9f\u0bcd\u0b9f sin x = 0
\n\u21d2 sin x = sin 0 \u21d2 x = n\u03c0, n \u2208 Z.
\n-10\u03c0 \u2264 x \u2264 10\u03c0, n \u0b86\u0ba9\u0ba4\u0bc1-1 \u0bb2\u0bbf\u0bb0\u0bc1\u0ba8\u0bcd\u0ba4\u0bc1-10 \u0bb2\u0bbf\u0bb0\u0bc1\u0ba8\u0bcd\u0ba4\u0bc1 +10 \u0b8e\u0b9f\u0bc1\u0ba4\u0bcd\u0ba4\u0bc1\u0b95\u0bcd \u0b95\u0bca\u0bb3\u0bcd\u0bb3\u0bb2\u0bbe\u0bae\u0bcd.
\n\u2234 x = n\u03c0, \u0b87\u0b99\u0bcd\u0b95\u0bc1 n = 0, \u00b11, \u00b12, \u00b13, \u00b14, \u00b15, \u00b16, \u00b17, \u00b18, \u00b19, \u00b110<\/p>\n

\"Samacheer<\/p>\n

(ii) sinx = -1
\n\u21d2 sin x = sin \\(\\left(\\frac{-\\pi}{2}\\right)\\) \u21d2 x = \\(\\frac{-\\pi}{2}\\), \\(\\frac{3 \\pi}{2}\\), \\(\\frac{7 \\pi}{2}\\), ….
\n\u21d2 x = (4n – 1)\\(\\frac{\\pi}{2}\\) ; n \u2208 z. \u21d2 x= (4n – 1)\\(\\frac{\\pi}{2}\\); n \u0b8e\u0b9f\u0bc1\u0ba4\u0bcd\u0ba4\u0bc1\u0b95\u0bcd \u0b95\u0bca\u0bb3\u0bcd\u0bb3\u0bc1\u0bae\u0bcd \u0bae\u0ba4\u0bbf\u0baa\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bcd 0, \u00b11, \u00b12, \u00b13 \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd \u00b14
\n\u0b86\u0ba4\u0bb2\u0bbe\u0bb2\u0bcd n = -4 \u0b8e\u0ba9\u0bbf\u0bb2\u0bcd, x = \\(\\frac{-17 \\pi}{2}\\) < -8\u03c0.<\/p>\n

Question 2.
\n\u0baa\u0bbf\u0ba9\u0bcd\u0bb5\u0bb0\u0bc1\u0bb5\u0ba9\u0bb5\u0bb1\u0bcd\u0bb1\u0bbf\u0ba9\u0bcd \u0b95\u0bbe\u0bb2\u0bae\u0bcd \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd \u0bb5\u0bc0\u0b9a\u0bcd\u0b9a\u0bc1 \u0b95\u0bbe\u0ba3\u0bcd\u0b95.
\n(i) y = sin 7x
\n(ii) y = – sin \\(\\left(\\frac{1}{3} x\\right)\\)
\n(iii) y = 4sin(-2x).
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1:
\n(i) \u0b95\u0bca\u0b9f\u0bc1\u0b95\u0bcd\u0b95\u0baa\u0bcd\u0baa\u0b9f\u0bcd\u0b9f y = sin 7x
\nsinx- \u0ba9\u0bcd \u0bb5\u0bc0\u0b9a\u0bcd\u0b9a\u0bc1 1 (\u0b9a\u0bc8\u0ba9\u0bcd \u0bb5\u0bb3\u0bc8\u0bb5\u0bb0\u0bc8\u0baf\u0bbf\u0ba9\u0bcd \u0bae\u0bc0\u0baa\u0bcd\u0baa\u0bc6\u0bb0\u0bc1 \u0bae\u0ba4\u0bbf\u0baa\u0bcd\u0baa\u0bc1 1]
\n\u21d2 sin 7x -\u0ba9\u0bcd \u0bb5\u0bc0\u0b9a\u0bcd\u0b9a\u0bc1\u0bae\u0bcd \u0b95\u0bc2\u0b9f 1.
\n\u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0bbf\u0ba9\u0bcd \u0b95\u0bbe\u0bb2\u0bae\u0bcd p \u0b8e\u0ba9\u0bbf\u0bb2\u0bcd f(x + p) = f(x).
\n\u0b9a\u0bc8\u0ba9\u0bcd \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0bbf\u0ba9\u0bcd \u0b95\u0bbe\u0bb2\u0bae\u0bcd 2\u03c0. \u0b86\u0ba4\u0bb2\u0bbe\u0bb2\u0bcd sin 7x \u0ba9\u0bcd \u0b95\u0bbe\u0bb2\u0bae\u0bcd \\(\\frac{2 \\pi}{7}\\) \u0b8f\u0ba9\u0bc6\u0ba9\u0bbf\u0bb2\u0bcd sin 7 \\(\\left(\\frac{2 \\pi}{7}\\right)\\) = sin 2\u03c0.<\/p>\n

(ii) y = – sin\\(\\left(\\frac{1}{3} x\\right)\\) sin x -\u0ba9\u0bcd \u0bb5\u0bc0\u0b9a\u0bcd\u0b9a\u0bc1 1
\n\u21d2 – sin\\(\\left(\\frac{1}{3} x\\right)\\)\u0ba9\u0bcd \u0bb5\u0bc0\u0b9a\u0bcd\u0b9a\u0bc1\u0bae\u0bcd \u0bae\u0bc7\u0bb2\u0bc1\u0bae\u0bcd 1.
\n– sin\\(\\left(\\frac{1}{3} x\\right)\\) \u0ba9\u0bcd \u0b95\u0bbe\u0bb2\u0bae\u0bcd \\(\\left(\\frac{1}{3} x\\right)\\) = 2\u03c0 \u21d2 x = 6\u03c0.<\/p>\n

\"Samacheer<\/p>\n

(iii) y = 4 sin (-2x)
\nsin x -\u0ba9\u0bcd \u0bb5\u0bc0\u0b9a\u0bcd\u0b9a\u0bc11
\n\u21d2 sin (-2x) -\u0ba9\u0bcd \u0bb5\u0bc0\u0b9a\u0bcd\u0b9a\u0bc1 1.
\n\u2234 4 sin(-2x)-\u0ba9\u0bcd \u0bb5\u0bc0\u0b9a\u0bcd\u0b9a\u0bc1 4 \u00d7 1 = 4.
\nsin(-2x) \u0ba9\u0bcd \u0b95\u0bbe\u0bb2\u0bae\u0bcd 2x = 2\u03c0 \u21d2 x = \\(\\frac{2 \\pi}{2}\\) = \u03c0<\/p>\n

Question 3.
\n0 \u2264 x \u2264 6\u03c0 \u0b8e\u0ba9\u0bc1\u0bae\u0bcd \u0baa\u0bcb\u0ba4\u0bc1 y = sin\\(\\left(\\frac{1}{3} x\\right)\\) \u0ba9\u0bcd \u0bb5\u0bb0\u0bc8\u0baa\u0b9f\u0bae\u0bcd \u0bb5\u0bb0\u0bc8\u0b95.
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1 :
\n\"Samacheer
\n\u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd 6\u03c0, 0) \u0b8e\u0ba9\u0bcd\u0bb1 \u0baa\u0bc1\u0bb3\u0bcd\u0bb3\u0bbf\u0b95\u0bb3\u0bc8 \u0b95\u0bc1\u0bb1\u0bbf
\n\"Samacheer<\/p>\n

Question 4.
\n\u0bae\u0ba4\u0bbf\u0baa\u0bcd\u0baa\u0bc1 \u0b95\u0bbe\u0ba3\u0bcd\u0b95
\n(i) \\(\\sin ^{-1}\\left(\\sin \\left(\\frac{2 \\pi}{3}\\right)\\right)\\)
\n(ii) \\(\\sin ^{-1}\\left(\\sin \\left(\\frac{5 \\pi}{4}\\right)\\right)\\)
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1:
\n(i) \"Samacheer<\/p>\n

\"Samacheer<\/p>\n

(ii) \"Samacheer<\/p>\n

Question 5.
\nx-\u0ba9\u0bcd \u0b8e\u0ba8\u0bcd\u0ba4 \u0bae\u0ba4\u0bbf\u0baa\u0bcd\u0baa\u0bbf\u0bb1\u0bcd\u0b95\u0bc1 sin x = sin-1<\/sup>x \u0b86\u0b95\u0bc1\u0bae\u0bcd?
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1:
\ny = sin-1<\/sup>x \u0b8e\u0ba9\u0bcd\u0b95.
\ny = 0, 0 = sin-1<\/sup>x \u0b8e\u0ba9\u0bbf\u0bb2\u0bcd
\n\u21d2 sin(0) = sin(sin-1<\/sup>(x))
\n\u21d2 sin 0 = x
\n\u21d2 x = 0
\n\u2234 x = 0 \u0b8e\u0ba9\u0bbf\u0bb2\u0bcd \u0bae\u0b9f\u0bcd\u0b9f\u0bc1\u0bae\u0bcd sin x = sin-1<\/sup>x<\/p>\n

\"Samacheer<\/p>\n

Question 6.
\n\u0baa\u0bbf\u0ba9\u0bcd\u0bb5\u0bb0\u0bc1\u0bb5\u0ba9\u0bb5\u0bb1\u0bcd\u0bb1\u0bbf\u0bb1\u0bcd\u0b95\u0bc1 \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0b95\u0bae\u0bcd \u0b95\u0bbe\u0ba3\u0bcd\u0b95.
\n(i) f(x) = sin-1<\/sup>\\(\\left(\\frac{x^{2}+1}{2 x}\\right)\\)
\n(ii) g(x) = 2 sin-1<\/sup>(2x – 1) – \\(\\frac{\\pi}{4}\\)
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1:
\n(i) \u0b95\u0bca\u0b9f\u0bc1\u0b95\u0bcd\u0b95\u0baa\u0bcd\u0baa\u0b9f\u0bcd\u0b9f f(x) = sin-1<\/sup>\\(\\left(\\frac{x^{2}+1}{2 x}\\right)\\)
\n\u0ba8\u0bae\u0b95\u0bcd\u0b95\u0bc1 \u0ba4\u0bc6\u0bb0\u0bbf\u0baf\u0bc1\u0bae\u0bcd sin(x) -\u0ba9\u0bcd \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0b95\u0bae\u0bcd [-1, 1]
\n\"Samacheer
\n(1) \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd (2) \u0bb2\u0bbf\u0bb0\u0bc1\u0ba8\u0bcd\u0ba4\u0bc1 \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0b95\u0bae\u0bcd = {-1, 1}<\/p>\n

\"Samacheer<\/p>\n

(ii) g(x) = 2 sin-1<\/sup>(2x – 1)-\\(\\frac{\\pi}{4}\\)
\nsin-1<\/sup>x \u0ba9\u0bcd \u0bb5\u0bb0\u0bc8\u0baf\u0bb1\u0bc8\u0baf\u0bbf\u0bb2\u0bbf\u0bb0\u0bc1\u0ba8\u0bcd\u0ba4\u0bc1
\n-1 \u2264 2x – 1 \u2264 1
\n\u21d2 -1+1 \u2264 2x \u2264 1 + 1 \u21d2 0 \u2264 2x \u2264 2
\n\u21d2 0 \u2264 x \u2264 1
\n\u2234 \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0b95\u0bae\u0bcd = [0, 1]<\/p>\n

\"Samacheer<\/p>\n

Question 7.
\n\u0bae\u0ba4\u0bbf\u0baa\u0bcd\u0baa\u0bc1 \u0b95\u0bbe\u0ba3\u0bcd\u0b95 sin-1<\/sup> (sin \\(\\frac{5 \\pi}{9}\\) cos\\(\\frac{\\pi}{9}\\) + cos \\(\\frac{5 \\pi}{9}\\) sin\\(\\frac{\\pi}{9}\\))
\n\u0ba4\u0bc0\u0bb0\u0bcd\u0bb5\u0bc1:
\n\"Samacheer<\/p>\n","protected":false},"excerpt":{"rendered":"

Tamilnadu State Board New Syllabus\u00a0Samacheer Kalvi 12th Maths Guide Pdf Chapter 4 \u0ba8\u0bc7\u0bb0\u0bcd\u0bae\u0bbe\u0bb1\u0bc1 \u0bae\u0bc1\u0b95\u0bcd\u0b95\u0bcb\u0ba3\u0bb5\u0bbf\u0baf\u0bb2\u0bcd \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bcd Ex 4.1 Textbook Questions and Answers, Notes. TN Board 12th Maths Solutions Chapter 4 \u0ba8\u0bc7\u0bb0\u0bcd\u0bae\u0bbe\u0bb1\u0bc1 \u0bae\u0bc1\u0b95\u0bcd\u0b95\u0bcb\u0ba3\u0bb5\u0bbf\u0baf\u0bb2\u0bcd \u0b9a\u0bbe\u0bb0\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bcd Ex 4.1 Question 1. x-\u0ba9\u0bcd \u0b85\u0ba9\u0bc8\u0ba4\u0bcd\u0ba4\u0bc1 \u0bae\u0ba4\u0bbf\u0baa\u0bcd\u0baa\u0bc1\u0b95\u0bb3\u0bc8\u0baf\u0bc1\u0bae\u0bcd \u0b95\u0bbe\u0ba3\u0bcd\u0b95. (i) -10\u03c0 \u2264 x \u2264 10\u03c0 \u0bae\u0bb1\u0bcd\u0bb1\u0bc1\u0bae\u0bcd sin x = 0 (ii) -8\u03c0 \u2264 x …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","footnotes":""},"categories":[8],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/50963"}],"collection":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/comments?post=50963"}],"version-history":[{"count":0,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/posts\/50963\/revisions"}],"wp:attachment":[{"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/media?parent=50963"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/categories?post=50963"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalviguru.com\/wp-json\/wp\/v2\/tags?post=50963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}