Properties Of Inverse Trigonometric Functions

The correct answer is D:

%5Cfrac%7B-%5Cpi%7D%7B10%7D

We have,

%5Csin%20%5E%7B-1%7D%5Cleft(%5Ccos%20%5Cfrac%7B53%20%5Cpi%7D%7B5%7D%5Cright)%3D%5Csin%20%5E%7B-1%7D%5Cleft%5B%5Ccos%20%5Cleft(10%20%5Cpi%2B%5Cfrac%7B3%20%5Cpi%7D%7B5%7D%5Cright)%5Cright%5D

%3D%5Csin%20%5E%7B-1%7D%5Cleft%5B%5Ccos%20%5Cleft(%5Cfrac%7B3%20%5Cpi%7D%7B5%7D%5Cright)%5Cright%5D

%5B%5Cbecause%20%5Ccos%20(2%20n%20%5Cpi%20%5Cpm%20%5Ctheta)%3D%5Ccos%20%5Ctheta%5D

%3D%5Csin%20%5E%7B-1%7D%5Cleft%5B%5Csin%20%5Cleft(%5Cfrac%7B%5Cpi%7D%7B2%7D-%5Cfrac%7B3%20%5Cpi%7D%7B5%7D%5Cright)%5Cright%5D

%3D%5Csin%20%5E%7B-1%7D%5Cleft%5B%5Csin%20%5Cleft(%5Cfrac%7B5%20%5Cpi-6%20%5Cpi%7D%7B10%7D%5Cright)%5Cright%5D

%3D%5Csin%20%5E%7B-1%7D%5Cleft%5B%5Csin%20%5Cleft(%5Cfrac%7B-%5Cpi%7D%7B10%7D%5Cright)%5Cright%5D%3D%5Cfrac%7B-%5Cpi%7D%7B10%7D

Chapter Questions
2 MCQs