Properties Of Inverse Trigonometric Functions

%5Csin%20%5E%7B-1%7D%20x-%5Csin%20%5E%7B-1%7D%202%20x%3D%5Cpm%20%5Cfrac%7B%5Cpi%7D%7B3%7D

%5CRightarrow%20%5Csin%20%5E%7B-1%7D%20x-%5Csin%20%5E%7B-1%7D%5Cleft(%5Cpm%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%5Cright)%3D%5Csin%20%5E%7B-1%7D%202%20x

%5CRightarrow%20%5Csin%20%5E%7B-1%7D%5Cleft%5Bx%20%5Csqrt%7B1-%5Cfrac%7B3%7D%7B4%7D%7D-%5Cleft(%5Cpm%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%20%5Csqrt%7B1-x%5E%7B2%7D%7D%5Cright)%5Cright%5D

%3D%5Csin%20%5E%7B-1%7D%202%20x

%5CRightarrow%20%5Cfrac%7Bx%7D%7B2%7D-%5Cleft(%5Cpm%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%20%5Csqrt%7B1-x%5E%7B2%7D%7D%5Cright)%3D2%20x

%5CRightarrow-%5Cleft(%5Cpm%20%5Csqrt%7B3%7D%20%5Csqrt%7B1-x%5E%7B2%7D%7D%5Cright)%3D3%20x

On squaring, both sides we get,

3%5Cleft(1-x%5E%7B2%7D%5Cright)%3D9%20x%5E%7B2%7D

%5CRightarrow%201-x%5E%7B2%7D%3D3%20x%5E%7B2%7D

%5CRightarrow%204%20x%5E%7B2%7D%3D1

%5CRightarrow%20x%3D%5Cpm%20%5Cfrac%7B1%7D%7B2%7D

Chapter Questions
2 MCQs