KCET2010MathematicsInverse Trigonometric Functions
If a>b>0, ⁻¹ a+b a-b =2 ⁻¹ x , then x is
Options
- A- b a+b
- Bb a+b
- C- a a+b
- Da a+b
Correct answer
B. b a+b
Step-by-step solution
If a>b>0, ⁻¹ ( a+b a-b )=2 ⁻¹ x ⁻¹ ( a - b a + b )=2 ⁻¹ x ⁻¹ ( 1- b a 1+ b a )=2 ⁻¹ x ⁻¹ 1-( b / a )² 1+( b / a )² =2 ⁻¹ x 2 ⁻¹( b / a )=2 ⁻¹ x [ 2 ⁻¹ x= ⁻¹ ( 1-x² 1+x² ) ] ⁻¹ ( b a+b )= ⁻¹ x [ ⁻¹ x= ⁻¹ x 1+x² ] x= b a+b