left square bracket sin to the power of negative 1 space end exponent cos to the power of negative 1 end exponent tan to the power of negative 1 end exponent x right square bracket equals 1         if[x] denotes greatest integer function then find the interval of values of x.
 

Asked by Devesh | 9th Nov, 2015, 02:58: PM

Expert Answer:

begin mathsize 11px style open square brackets sin to the power of negative 1 end exponent cos to the power of negative 1 end exponent tan to the power of negative 1 end exponent straight x close square brackets equals 1 rightwards double arrow sin to the power of negative 1 end exponent cos to the power of negative 1 end exponent tan to the power of negative 1 end exponent straight x space element of space left square bracket 1 comma 2 right parenthesis rightwards double arrow cos to the power of negative 1 end exponent tan to the power of negative 1 end exponent straight x space will space vary space between space sin space 1 space and space sin space 2 space left parenthesis excluding space sin space 2 right parenthesis sin space function space value space increases space from space sin 1 space to space reach space 1 space at space straight pi divided by 2 space and space then space decrease space up space to space sin space 2 space in space this space range. sin space 1 space less than space sin space 2 space less than space 1 space left parenthesis from space graph space of space sinx space and space symmetry right parenthesis Hence comma space cos to the power of negative 1 end exponent tan to the power of negative 1 end exponent straight x element of space left square bracket sin 1 comma space 1 right square bracket rightwards double arrow tan to the power of negative 1 end exponent straight x space will space vary space between space cos space left parenthesis sin 1 right parenthesis space and space cos 1 sin 1 space less than space 1 rightwards double arrow cos space left parenthesis sin 1 right parenthesis space greater than space cos 1 rightwards double arrow tan to the power of negative 1 end exponent straight x element of open square brackets cos 1 comma space cos space left parenthesis sin 1 right parenthesis space close square brackets 0 space less than space cos 1 space less than cos space left parenthesis sin 1 right parenthesis space less than space straight pi over 2 In space this space interval comma space tan space is space an space increasin space function. rightwards double arrow straight x element of open square brackets tan left parenthesis cos 1 right parenthesis comma space tan left parenthesis cos space left parenthesis sin 1 right parenthesis right parenthesis space close square brackets space end style

Answered by satyajit samal | 9th Nov, 2015, 07:51: PM