solve equation for x sin1 x cos1xpi3 Thank youSolutionsin1x

solve equation for x: sin^-1 (x) - cos^-1(x)=-(pi/3)

Thank you.

Solution

sin^-1x-cos^-1x=-pi/3

We have to use the following relationship

sin^-1x+ cos^-1x=pi/2

sin^-1x= pi/2-cos-1x

pi/2 - cos^-1x - cos^-1x=-pi/3

pi/2 - 2cos^-1x=-pi/3

pi/2+pi/3 = 2cos^-1x

5pi/6=2cos^-1x

cos^-1x= 5pi/12

x=cos(5pi/12)=(sqrt3    -    1)/2sqrt2 = sqrt2(sqrt3   -    1)/4