{"id":10318,"date":"2024-02-26T17:37:50","date_gmt":"2024-02-26T12:07:50","guid":{"rendered":"https:\/\/tsboardsolutions.in\/?p=10318"},"modified":"2024-02-27T17:55:55","modified_gmt":"2024-02-27T12:25:55","slug":"ts-inter-1st-year-maths-1a-inverse-trigonometric-functions-important-questions","status":"publish","type":"post","link":"https:\/\/tsboardsolutions.in\/ts-inter-1st-year-maths-1a-inverse-trigonometric-functions-important-questions\/","title":{"rendered":"TS Inter 1st Year Maths 1A Inverse Trigonometric Functions Important Questions"},"content":{"rendered":"

Students must practice these\u00a0TS Inter 1st Year Maths 1A Important Questions<\/a> Chapter 8 Inverse Trigonometric Functions to help strengthen their preparations for exams.<\/p>\n

TS Inter 1st Year Maths 1A Inverse Trigonometric Functions Important Questions<\/h2>\n

Question 1.
\nProve that
\n\"TS
\nSolution:
\n\"TS<\/p>\n

\"TS<\/p>\n

Question 2.
\nFind the values of the following.<\/p>\n

(i)\u00a0\\(\\sin ^{-1}\\left(-\\frac{1}{2}\\right)\\)
\nSolution:
\n\\(\\sin ^{-1}\\left(-\\frac{1}{2}\\right)=-\\sin ^{-1}\\left(\\frac{1}{2}\\right)=-\\frac{\\pi}{6}\\)<\/p>\n

(ii) \\(\\cos ^{-1}\\left(-\\frac{\\sqrt{3}}{2}\\right)\\)
\nSolution:
\n\"TS<\/p>\n

(iii) \\(\\tan ^{-1}\\left(\\frac{1}{\\sqrt{3}}\\right)\\)
\nSolution:
\n\\(\\tan ^{-1}\\left(\\frac{1}{\\sqrt{3}}\\right)=\\tan ^{-1}\\left(\\tan \\frac{\\pi}{6}\\right)=\\frac{\\pi}{6}\\)<\/p>\n

\"TS<\/p>\n

(iv) cot-1<\/sup>\u00a0(-1)
\nSolution:
\n\"TS<\/p>\n

(v) sec -1\u00a0 <\/sup> \\((-\\sqrt{2})\\)
\nSolution:
\n\"TS<\/p>\n

(vi) Cosec -1\u00a0<\/sup> \\(\\left(\\frac{2}{\\sqrt{3}}\\right)\\)
\nSolution:
\n\"TS<\/p>\n

Question 3.
\nFind the values of the following.<\/p>\n

(i) sin-1 <\/sup> \\(\\left(\\sin \\frac{4 \\pi}{3}\\right)\\)
\nSolution:
\n\"TS<\/p>\n

(ii) \\(\\tan ^{-1}\\left(\\tan \\frac{4 \\pi}{3}\\right)\\)
\nSolution:
\n\"TS<\/p>\n

\"TS<\/p>\n

Question 4.
\nFind the values of the following.<\/p>\n

(i) \\(\\sin \\left(\\cos ^{-1} \\frac{5}{13}\\right)\\)
\nSolution:
\n\"TS<\/p>\n

(ii) \\(\\tan \\left(\\sec ^{-1} \\frac{25}{7}\\right)\\)
\nSolution:
\n\"TS<\/p>\n

(iii) \\(\\cos \\left(\\tan ^{-1} \\frac{24}{7}\\right)\\)
\nSolution:
\n\"TS<\/p>\n

Question 5.
\nFind the values of the following.<\/p>\n

(i) \\(\\sin ^2\\left(\\tan ^{-1} \\frac{3}{4}\\right)\\)
\nSolution:
\n\"TS<\/p>\n

(ii) \\(\\sin \\left(\\frac{\\pi}{2}-\\sin ^{-1}\\left(-\\frac{4}{5}\\right)\\right)\\)
\nSolution:
\n\"TS<\/p>\n

(iii) \\(\\cos \\left(\\cos ^{-1}\\left(-\\frac{2}{3}\\right)-\\sin ^{-1}\\left(\\frac{2}{3}\\right)\\right)\\)
\nSolution:
\n\"TS<\/p>\n

\"TS<\/p>\n

(iv) sec2<\/sup> (cot-1 <\/sup>3) + cosec2<\/sup> (tan-1<\/sup> 2)
\nSolution:
\n\"TS<\/p>\n

Question 6.
\nFind the value of \\(\\cot ^{-1}\\left(\\frac{1}{2}\\right)+\\cot ^{-1}\\left(\\frac{1}{3}\\right)\\)
\nSolution:
\n\"TS<\/p>\n

Question 7.
\nProve that
\n\\(\\sin ^{-1}\\left(\\frac{4}{5}\\right)+\\sin ^{-1}\\left(\\frac{7}{25}\\right)=\\sin ^{-1}\\left(\\frac{117}{125}\\right)\\)
\nSolution:
\n\"TS<\/p>\n

\"TS<\/p>\n

Question 8.
\nIf x \u2208(-1, 1) prove that 2 tan-1<\/sup> x = \\(\\tan ^{-1}\\left(\\frac{2 x}{1-x^2}\\right)\\)
\nSolution:
\nGiven x \u2208 (-1,1) and it tan-1<\/sup> x = a then tan \u03b1 = x and
\n\"TS<\/p>\n

Question 9.
\nProve that \\(\\sin ^{-1}\\left(\\frac{4}{5}\\right)+\\sin ^{-1}\\left(\\frac{5}{13}\\right) +\\sin ^{-1}\\left(\\frac{16}{65}\\right)=\\frac{\\pi}{2}\\)
\nSolution:
\n\"TS<\/p>\n

Question 10.
\nProve that cot-1<\/sup> 9+ cosec-1<\/sup> \\( \\frac{\\sqrt{41}}{4}=\\frac{\\pi}{4}\\)
\nSolution:
\n\"TS<\/p>\n

\"TS
\n
\nQuestion 11.
\nShow that cot \\(\\begin{aligned} \\cot \\left(\\operatorname{Sin}^{-1} \\sqrt{\\frac{13}{17}}\\right) \\\\ = \\sin \\left(\\operatorname{Tan}^{-1}\\left(\\frac{2}{3}\\right)\\right) \\end{aligned}\\)
\nSolution:
\n\"TS
\n<\/span><\/p>\n

Question 12.
\nFind the value of \\(tan \\left[2 \\operatorname{Tan}^{-1}\\left(\\frac{1}{5}\\right)-\\frac{\\pi}{4}\\right]\\)
\nSolution:
\n\"TS<\/p>\n

Question 13.
\nProve that \\(\\operatorname{Sin}^{-1}\\left(\\frac{4}{5}\\right)+2 \\operatorname{Tan}^{-1}\\left(\\frac{1}{3}\\right)=\\frac{\\pi}{2}\\)
\nSolution:
\n\"TS<\/p>\n

\"TS<\/p>\n

Question 14.
\nIf sin-1 <\/sup>x + sin-1<\/sup> y + sin-1<\/sup> z = \u03c0, then prove that x4<\/sup> + y4<\/sup> + z4<\/sup> + 4x2<\/sup>y2<\/sup>z2 <\/sup>= 2 (x2<\/sup>y2<\/sup> + y2<\/sup>z2 <\/sup>+ z2<\/sup>x2<\/sup>)
\nSolution:
\nLet sin-1<\/sup> x = A, sin-1<\/sup> y = B and sin-1<\/sup>z = C
\nthen A+B+C = \u03c0 …………………..(1)
\nand sinA = x, sin B = y, sin C = z
\nNow A+B = \u03c0 – c
\n\"TS<\/p>\n

Question 15.
\nIf \\(\\operatorname{Cos}^{-1}\\left(\\frac{p}{a}\\right)+\\operatorname{Cos}^{-1}\\left(\\frac{q}{b}\\right)\\) =\u03b1 the prove that
\n\"TS
\nSolution:
\n\"TS
\n\"TS<\/p>\n

\"TS<\/p>\n

Question 16.
\nSolve \\(\\sin ^{-1}\\left(\\frac{5}{x}\\right)+\\sin ^{-1}\\left(\\frac{12}{x}\\right)=\\frac{\\pi}{2},(x>0)\\)
\nSolution:
\n\"TS<\/p>\n

Question 17.
\nSolve
\n\"TS
\nSolution:
\n\"TS<\/p>\n

Question 18.
\nSolve \\(\\operatorname{Sin}^{-1} x+\\operatorname{Sin}^{-1} 2 x=\\frac{\\pi}{3}\\)
\nSolution:
\n\"TS
\nwhen \\(x=-\\frac{\\sqrt{3}}{2 \\sqrt{7}}\\) value is not admissible
\nSince sin-1<\/sup> x and sin-1<\/sup> 2x are negative
\nHence \\(x=-\\frac{\\sqrt{3}}{2 \\sqrt{7}}\\)<\/p>\n

\"TS<\/p>\n

Question 19.
\nIf sin [2 Cos-1<\/sup> (cot (2 Tan-1<\/sup>x)}] = 0 find x.
\nSolution:
\n\"TS<\/p>\n

Question 20.
\nProve that
\n\"TS
\nSolution:
\nLet cot-1 <\/sup>x=\u03b8 then cot \u03b8 = x and \u03b8 <x<\u03c0
\n\u2234 sin (cot-1<\/sup>x) = sin\u03b8 = \\(\\frac{1}{\\operatorname{cosec} \\theta}\\)
\n\"TS<\/p>\n

\"TS<\/p>\n

Question 21.
\nShow that sec2<\/sup> (tan-1<\/sup>) + cosec2<\/sup> (cot-1<\/sup> 2) = 10.
\nSolution:
\n[1 + tan2<\/sup> (tan-1<\/sup>(2)] + [1+ cot2<\/sup>\u00a0(cot-1<\/sup>(2))]
\n= 1 + 4 + 1 + 4 = 10<\/p>\n","protected":false},"excerpt":{"rendered":"

Students must practice these\u00a0TS Inter 1st Year Maths 1A Important Questions Chapter 8 Inverse Trigonometric Functions to help strengthen their preparations for exams. TS Inter 1st Year Maths 1A Inverse Trigonometric Functions Important Questions Question 1. Prove that Solution: Question 2. Find the values of the following. (i)\u00a0 Solution: (ii) Solution: (iii) Solution: (iv) cot-1\u00a0(-1) … Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/10318"}],"collection":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/comments?post=10318"}],"version-history":[{"count":10,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/10318\/revisions"}],"predecessor-version":[{"id":10532,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/10318\/revisions\/10532"}],"wp:attachment":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/media?parent=10318"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/categories?post=10318"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/tags?post=10318"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}