-->

Inverse Trigonometric Functions

Question
CBSEENMA12032752

Solve, the following equations;
2 tan–1(cos x) = tan–1t (2 cosec x)

Solution
2 tan –1(cos x) = tan –1(2 cosec x)

rightwards double arrow space space space tan to the power of negative 1 end exponent open parentheses fraction numerator 2 space cos space straight x space over denominator 1 minus space cos squared space straight x end fraction close parentheses equals space tan to the power of negative 1 end exponent open parentheses fraction numerator 2 over denominator sin space straight x end fraction close parentheses space space space space space space space space space space space space open square brackets space because space 2 space tan to the power of negative 1 end exponent space straight x equals space tan to the power of negative 1 end exponent space fraction numerator 2 straight x over denominator 1 minus straight x squared end fraction close square brackets

rightwards double arrow space space space tan to the power of negative 1 end exponent open parentheses fraction numerator 2 space cos space straight x over denominator sin squared space straight x end fraction close parentheses equals space tan to the power of negative 1 end exponent open parentheses fraction numerator 2 over denominator sin space straight x end fraction close parentheses space space space space space space space space space space space space space space space space space rightwards double arrow space fraction numerator 2 space cos space straight x over denominator sin squared space straight x end fraction equals fraction numerator 2 over denominator sin space straight x end fraction
rightwards double arrow space space space 2 space cos space straight x space equals space 2 space sin space straight x space space space space space space space space space space space space rightwards double arrow space space space tan space straight x space equals space 1 space space space space space space space rightwards double arrow space space straight x equals straight pi over 4 space space

Some More Questions From Inverse Trigonometric Functions Chapter