Inverse Trigonometric Functions

Question

Prove that $tan to the power of negative 1 end exponent open parentheses 1 half close parentheses plus tan to the power of negative 1 end exponent open parentheses 1 fifth close parentheses plus tan to the power of negative 1 end exponent open parentheses 1 over 8 close parentheses space equals straight pi over 4$

Solution

We know that:
$tan to the power of negative 1 end exponent straight x plus tan to the power of negative 1 end exponent straight y space equals space tan to the power of negative 1 end exponent fraction numerator straight x plus straight y over denominator 1 minus xy end fraction comma space xy less than 1$
We have:
$tan to the power of negative 1 end exponent open parentheses 1 half close parentheses plus tan to the power of negative 1 end exponent open parentheses 1 fifth close parentheses plus tan to the power of negative 1 end exponent open parentheses 1 over 8 close parentheses equals open square brackets tan to the power of negative 1 end exponent open parentheses 1 half close parentheses plus tan to the power of negative 1 end exponent open parentheses 1 fifth close parentheses plus tan to the power of negative 1 end exponent open parentheses 1 over 8 close parentheses close square brackets equals tan to the power of negative 1 end exponent open parentheses fraction numerator begin display style 1 half end style plus begin display style 1 fifth end style over denominator 1 minus begin display style 1 half end style cross times begin display style 1 fifth end style end fraction close parentheses plus tan to the power of negative 1 end exponent open parentheses 1 over 8 close parentheses space space space open parentheses because space space 1 half cross times 1 fifth less than 1 close parentheses equals tan to the power of negative 1 end exponent open parentheses 7 over 9 close parentheses plus tan to the power of negative 1 end exponent open parentheses 1 over 8 close parentheses$
$equals tan to the power of negative 1 end exponent fraction numerator begin display style 7 over 9 end style plus begin display style 1 over 8 end style over denominator 1 minus begin display style 7 over 9 end style cross times begin display style 1 over 8 end style end fraction equals tan to the power of negative 1 end exponent fraction numerator 56 plus 9 over denominator 72 minus 7 end fraction space open parentheses because 7 over 9 cross times 1 over 8 less than 1 close parentheses equals tan to the power of negative 1 end exponent 65 over 65 equals tan to the power of negative 1 end exponent 1 equals straight pi over 4 Hence comma space tan to the power of negative 1 end exponent open parentheses 1 half close parentheses plus tan to the power of negative 1 end exponent open parentheses 1 fifth close parentheses plus tan to the power of negative 1 end exponent open parentheses 1 over 8 close parentheses equals straight pi over 4$

For Daily Free Study Material Join wiredfaculty

Inverse Trigonometric Functions

Some More Questions From Inverse Trigonometric Functions Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction