{"id":7185,"date":"2024-01-17T16:07:04","date_gmt":"2024-01-17T10:37:04","guid":{"rendered":"https:\/\/tsboardsolutions.in\/?p=7185"},"modified":"2024-01-19T17:49:03","modified_gmt":"2024-01-19T12:19:03","slug":"ts-inter-1st-year-maths-1a-solutions-chapter-9-ex-9a","status":"publish","type":"post","link":"https:\/\/tsboardsolutions.in\/ts-inter-1st-year-maths-1a-solutions-chapter-9-ex-9a\/","title":{"rendered":"TS Inter 1st Year Maths 1A Solutions Chapter 9 Hyperbolic Functions Ex 9(a)"},"content":{"rendered":"

Students must practice these\u00a0TS Intermediate Maths 1A Solutions<\/a> Chapter 9 Hyperbolic Functions Ex 9(a) to find a better approach to solving the problems.<\/p>\n

TS Inter 1st Year Maths 1A Hyperbolic Functions Solutions Exercise 9(a)<\/h2>\n

I.
\nQuestion 1.
\nIf sinh x = \\(\\frac{3}{4}\\) find cosh (2x) and sinh (2x). (May 2014, Mar.’14, \u201912)
\nAnswer:
\nGiven sinh x = \\(\\frac{3}{4}\\)
\nand we have cosh2<\/sup> x – sinh2<\/sup> x = 1
\n\"TS<\/p>\n

\"TS<\/p>\n

Question 2.
\nIf sinhx = 3, then show that
\nx = loge<\/sub>(3 + \u221a10) (Board New Model Paper).
\nAnswer:
\nGiven sin hx = 3
\n\u21d2 x = sinh-1<\/sup> 3 = loge<\/sub> (3 + \\(\\sqrt{3^2+1}\\))
\n= loge<\/sub> (3 + \u221a10)
\n(\u2235 sinh x = log (x + \\(\\sqrt{x^2+1}\\)) \u2200 x \u2208 R)<\/p>\n

Question 3.
\nProve that
\n(i) tanh (x – y) = \\(\\frac{\\tanh x-\\tanh y}{1-\\tanh x \\tanh y}\\)
\nAnswer:
\n\"TS<\/p>\n

(ii) coth (x – y) = \\(\\frac{{coth} x \\cdot {coth} y-1}{{coth} y-{coth} x}\\)
\nAnswer:
\n\"TS<\/p>\n

Question 4.
\nProve that
\n(i) (cosh x – sinh x)n<\/sup>
\n= cosh (nx) – sinh (nx) for any n \u2208R.
\nAnswer:
\n\"TS<\/p>\n

(ii) (cosh x + sinh x)n<\/sup> = cosh (nx) + sinh (nx) for any n \u2208 R.
\nAnswer:
\n\"TS<\/p>\n

\"TS<\/p>\n

Question 5.
\nProve that
\n\\(\\frac{\\tanh x}{{sech} x-1}+\\frac{\\tanh x}{{sech} x+1}\\) = -2cosechx for x \u2260 0.
\nAnswer:
\n\"TS<\/p>\n

Question 6.
\nProve that \\(\\frac{\\cosh x}{1-\\tanh x}+\\frac{\\sinh x}{1-{coth} x}\\) = sinhx + coshx for x \u2260 0.
\nAnswer:
\n\"TS<\/p>\n

Question 7.
\nFor any x \u2208 R, prove that cosh4<\/sup> x – sinh4<\/sup> x = cosh 2x.
\nAnswer:
\ncosh4<\/sup> x – sinh4<\/sup> x
\n= (cosh2<\/sup> x)2<\/sup> – (sinh2<\/sup> x)2<\/sup>
\n= (cosh2<\/sup> x + sinh2<\/sup> x) (cosh2<\/sup> x – sinh2<\/sup> x)
\n= cosh 2x (1) = cosh 2x<\/p>\n

\"TS<\/p>\n

Question 8.
\nIf u = loge<\/sub> \\(\\left\\{\\tan \\left(\\frac{\\pi}{4}+\\frac{\\theta}{2}\\right)\\right\\}\\) and if cos \u03b8 > 0 then prove that cosh u = sec \u03b8
\nAnswer:
\n\"TS<\/p>\n","protected":false},"excerpt":{"rendered":"

Students must practice these\u00a0TS Intermediate Maths 1A Solutions Chapter 9 Hyperbolic Functions Ex 9(a) to find a better approach to solving the problems. TS Inter 1st Year Maths 1A Hyperbolic Functions Solutions Exercise 9(a) I. Question 1. If sinh x = find cosh (2x) and sinh (2x). (May 2014, Mar.’14, \u201912) Answer: Given sinh x … Read more<\/a><\/p>\n","protected":false},"author":3,"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\/7185"}],"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\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/comments?post=7185"}],"version-history":[{"count":4,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/7185\/revisions"}],"predecessor-version":[{"id":7439,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/7185\/revisions\/7439"}],"wp:attachment":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/media?parent=7185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/categories?post=7185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/tags?post=7185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}