Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 12-science Answered

Q:Write into simplest form
                                 c o t to the power of negative 1 end exponent left parenthesis square root of 1 plus x squared end root minus x right parenthesis .
Asked by Ravi consul | 15 Mar, 2015, 08:20: PM
answered-by-expert Expert Answer
l e t space x equals space tan space theta theta equals tan to the power of negative 1 end exponent x comma c o t to the power of negative 1 end exponent open parentheses square root of 1 plus x squared end root minus x close parentheses equals c o t to the power of negative 1 end exponent open parentheses square root of 1 plus tan squared theta end root minus tan space theta close parentheses equals c o t to the power of negative 1 end exponent open parentheses s e c space theta minus tan space theta close parentheses equals c o t to the power of negative 1 end exponent open parentheses fraction numerator 1 over denominator cos space theta end fraction minus fraction numerator sin space theta over denominator cos space theta end fraction close parentheses equals c o t to the power of negative 1 end exponent open parentheses fraction numerator 1 minus sin space theta over denominator cos space theta end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses fraction numerator cos space theta over denominator 1 minus sin space theta end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses fraction numerator cos space squared begin display style theta over 2 end style minus sin squared begin display style theta over 2 end style over denominator cos squared begin display style theta over 2 end style plus sin squared begin display style theta over 2 end style minus 2 sin begin display style theta over 2 end style cos begin display style theta over 2 end style end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style open parentheses cos theta over 2 minus sin theta over 2 close parentheses open parentheses cos theta over 2 plus sin theta over 2 close parentheses end style over denominator begin display style open parentheses cos theta over 2 minus sin theta over 2 close parentheses squared end style end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style open parentheses cos theta over 2 plus sin theta over 2 close parentheses end style over denominator begin display style open parentheses cos theta over 2 minus sin theta over 2 close parentheses end style end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style bevelled fraction numerator begin display style open parentheses cos theta over 2 plus sin theta over 2 close parentheses end style over denominator cos space begin display style theta over 2 end style end fraction end style over denominator begin display style bevelled fraction numerator begin display style open parentheses cos theta over 2 minus sin theta over 2 close parentheses end style over denominator cos space begin display style theta over 2 end style end fraction end style end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style open parentheses 1 plus tan theta over 2 close parentheses end style over denominator begin display style open parentheses 1 minus tan theta over 2 close parentheses end style end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style open parentheses tan space straight pi over 4 plus tan theta over 2 close parentheses end style over denominator begin display style open parentheses 1 minus tan space straight pi over 4. tan theta over 2 close parentheses end style end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses tan open parentheses straight pi over 4 plus theta over 2 close parentheses close parentheses space space space open square brackets S i n c e comma space tan to the power of negative 1 end exponent open parentheses tan space theta close parentheses equals theta close square brackets equals straight pi over 4 plus fraction numerator tan to the power of negative 1 end exponent x over denominator 2 end fraction
Answered by Prasenjit Paul | 16 Mar, 2015, 12:32: PM

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 12-science - Maths
solve it
question image
Asked by sdmbotch1123 | 19 Sep, 2023, 01:53: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Solve it pls.
question image
Asked by sdmbotch1123 | 10 Apr, 2023, 10:55: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Evaluate 3 sin -1 (1/root 2) + 2 cos -1 (root3/2) + cos-1(0)
Asked by varma.renu9481 | 13 Mar, 2023, 11:51: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Sin^-1x = cos^-1x, 0<x<1. Solve  
question image
Asked by w3ctiger | 12 Feb, 2023, 11:55: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
tan¹x + tan¹y=π+tan¹(x+y/1-xy), xy>1;x, y>0
Asked by joymaibam38 | 26 Dec, 2021, 09:04: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
peinciple branch od sec -¹ x
Asked by naikmanjuank | 17 Sep, 2020, 11:48: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
tan^-1x-1/x-2+tan^-1x+1/x+2=pi/4.find value of x.   
Asked by sshas3199 | 23 Aug, 2020, 09:24: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
  Consider the equation . Choose the CORRECT option(s). The sum of all solutions = 0< The number of solutions = 2< The number of solution = 1< The sum of squares of all solutions = 1<
Asked by harshsharma2531 | 09 Aug, 2020, 09:28: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Sin(sin-11/5+cos-1x)=1 Find value of x?
Asked by raiannu064 | 16 Jan, 2020, 01:03: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Plz solve (x) part Find the value of x
question image
Asked by lovemaan5500 | 04 Jan, 2020, 11:12: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×