+91-8076753736 support@wiredfaculty.com

Sponsor Area

Inverse Trigonometric Functions

Question

Wired Faculty App

Simplify

$tan to the power of negative 1 end exponent open parentheses fraction numerator square root of 1 plus x squared end root minus 1 over denominator x end fraction close parentheses$

Solution

Let space straight z equals bold tan to the power of bold minus bold 1 end exponent open parentheses fraction numerator square root of bold 1 bold plus bold x to the power of bold 2 end root bold minus bold 1 over denominator bold x end fraction close parentheses Put space space space space space space space straight x equals tan space straight theta therefore space space space space space space straight z equals tan to the power of negative 1 end exponent open parentheses fraction numerator square root of 1 plus tan squared space straight theta minus 1 end root over denominator tan space straight theta end fraction close parentheses equals tan to the power of negative 1 end exponent open parentheses fraction numerator sec space straight theta minus 1 over denominator tan space straight theta end fraction close parentheses equals tan to the power of negative 1 end exponent open square brackets fraction numerator begin display style fraction numerator 1 over denominator cos space straight theta end fraction end style minus 1 over denominator begin display style fraction numerator sin space straight theta over denominator cos space straight theta end fraction end style end fraction close square brackets space space space space space space space space space space equals space tan to the power of negative 1 end exponent open parentheses fraction numerator 1 minus cos space straight theta over denominator sin space straight theta end fraction close parentheses equals tan to the power of negative 1 end exponent open square brackets fraction numerator 2 space sin squared space begin display style straight theta over 2 end style over denominator 2 space sin space begin display style straight theta over 2 end style space cos space 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 parentheses tan straight theta over 2 close parentheses equals straight theta over 2 equals 1 half tan to the power of negative 1 end exponent space straight x

Some More Questions From Inverse Trigonometric Functions Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation