Manipal MET2010MathematicsInverse Trigonometric Functions
2 ⁻¹ ( cosec ⁻¹ x- ⁻¹ x ) is equal to
Options
- A⁻¹ x
- B⁻¹ 1 x
- C⁻¹ x
- DNone of these
Correct answer
C. ⁻¹ x
Step-by-step solution
The given expression aligned & =2 ⁻¹ [ cosec ⁻¹ x- ⁻¹ x ] = & 2 ⁻¹ [ cosec cosec ⁻¹ 1+x^2 x . .- ⁻¹ ( 1 x ) ] = & 2 ⁻¹ [ 1+x^2 x - 1 x ]=2 ⁻¹ [ 1+x^2 -1 x ] = & 2 ⁻¹ [ -1 ] [putting x= ] = & ⁻¹ [ 1- ] = & 2 ⁻¹ [ 2 2 2 2 2 ] = & 2 ⁻¹ 2 =2 2 = = ⁻¹ x aligned