Find the values of each of the following:
8. (tan^{-1}[2cos(2sin^{-1}{frac{1}{2}})]).
Inverse Trigonometric Functions
Exercise 2.2
Class 12
Inverse Trigonometric Functions
Exercise 2.2
1. (3sin^{-1}{x}=sin^{-1}(3x-4x^3)), (xin[-frac{1}{2},frac{1}{2}]).
2. (3cos^{-1}{x}=cos^{-1}(4x^3-3x)), (xin[frac{1}{2},1]).
Write the following functions in the simplest form:
3. (tan^{-1}{frac{sqrt{1+x^2}-1}{x}}), (xne {0}).
4. (tan^{-1}(sqrt{frac{1-cosx}{1+cosx}})),(0<x<pi).
5. (tan^{-1}(frac{cosx-sinx}{cosx+sinx})), (-frac{pi}{4}<x<frac{3pi}{4}).
6. (tan^{-1}{frac{x}{sqrt{a^2-x^2}}}), (|x|<a).
7. (tan^{-1}(frac{3a^2x-x^3}{a^3-3ax^2})), (a>0;-frac{a}{sqrt3}<x<frac{a}{sqrt3}).
Find the values of each of the following:
8. (tan^{-1}[2cos(2sin^{-1}{frac{1}{2}})]).
9. (tan^{-1}[sin^{-1}{frac{2x}{1+x^2}}+cos^{-1}{frac{1-y^2}{1+y^2}}]), (|x|<1, y>0) and (xy<1).
Find the values of each of the expressions in Exercises 10 to 15.
10. (sin^{-1}(sin{frac{2pi}{3}})).
11. (tan^{-1}(tan{frac{3pi}{4}})).
12. (tan(sin^{-1}{frac{3}{5}}+cot^{-1}{frac{3}{2}})).
13. (cos^{-1}(cos{frac{7pi}{6}})).
14. (sin(frac{pi}{3}-sin^{-1}(-frac{1}{2}))).
15. (tan^{-1}{sqrt3}-cot^{-1}({-sqrt3})) is equal to:
