+91-8076753736 support@wiredfaculty.com
logo
logo

A PHP Error was encountered

Severity: Notice

Message: Undefined variable: temp_qds

Filename: Questions_Page/Ncert_Question.php

Line Number: 320

Backtrace:

File: /home/wiredfa1/public_html/application/views/final/Questions_Page/Ncert_Question.php
Line: 320
Function: _error_handler

File: /home/wiredfa1/public_html/application/controllers/Home.php
Line: 235
Function: view

File: /home/wiredfa1/public_html/index.php
Line: 315
Function: require_once

Sponsor Area

Continuity And Differentiability

Question
CBSEENMA12035233
Wired Faculty App

Differentiate space colon space tan to the power of negative 1 end exponent open parentheses fraction numerator square root of 1 plus straight x end root minus square root of 1 minus straight x end root over denominator square root of 1 plus straight x end root plus square root of 1 minus straight x end root end fraction close parentheses space straight w. straight r. straight t. straight x.

Solution
Let space straight y equals space tan to the power of negative 1 end exponent open parentheses fraction numerator square root of 1 plus straight x end root minus square root of 1 minus straight x end root over denominator square root of 1 plus straight x end root plus square root of 1 minus straight x end root end fraction close parentheses Put space straight x equals cos space straight theta therefore space space space straight y equals space tan to the power of negative 1 end exponent open parentheses fraction numerator square root of 1 plus cosθ end root minus square root of 1 minus cosθ end root over denominator square root of 1 plus cosθ end root plus square root of 1 minus cosθ end root end fraction close parentheses equals space tan to the power of negative 1 end exponent open square brackets fraction numerator square root of 2 cos squared straight theta over 2 end root minus square root of 2 sin squared straight theta over 2 end root over denominator square root of 2 cos squared straight theta over 2 end root plus square root of 2 sin squared straight theta over 2 end root end fraction close square brackets space space space space space space space space space equals space tan to the power of negative 1 end exponent open square brackets fraction numerator square root of 2 cos straight theta over 2 minus square root of 2 sin straight theta over 2 over denominator square root of 2 cos straight theta over 2 plus square root of 2 sin straight theta over 2 end fraction close square brackets equals space tan to the power of negative 1 end exponent open square brackets fraction numerator cos straight theta over 2 minus sin straight theta over 2 over denominator cos straight theta over 2 plus sin straight theta over 2 end fraction close square brackets space space space space space space space space space equals space tan to the power of negative 1 end exponent open square brackets fraction numerator begin display style fraction numerator cos begin display style straight theta over 2 end style over denominator cos begin display style straight theta over 2 end style end fraction end style minus begin display style fraction numerator sin begin display style straight theta over 2 end style over denominator cos begin display style straight theta over 2 end style end fraction end style over denominator begin display style fraction numerator cos begin display style straight theta over 2 end style over denominator cos begin display style straight theta over 2 end style end fraction end style plus begin display style fraction numerator sin begin display style straight theta over 2 end style over denominator cos begin display style straight theta over 2 end style end fraction end style end fraction close square brackets equals space tan to the power of negative 1 end exponent open square brackets fraction numerator 1 minus tan begin display style straight theta over 2 end style over denominator 1 plus tan begin display style straight theta over 2 end style end fraction close square brackets space space space space space space space space space space equals tan to the power of negative 1 end exponent open square brackets tan open parentheses straight pi over 4 minus straight theta over 2 close parentheses close square brackets equals straight pi over 4 minus straight theta over 2 therefore space straight y equals straight pi over 4 minus 1 half. cos to the power of negative 1 end exponent straight x dy over dx equals 0 minus 1 half. fraction numerator negative 1 over denominator square root of 1 minus straight x squared end root end fraction

Some More Questions From Continuity and Differentiability Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation