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COMEDK2016MathematicsInverse Trigonometric Functions

If a>b>0 , then the value of ⁻¹ ( a b )+ ⁻¹ ( a+b a-b ) depends on

Options

  1. Aneither a nor b
  2. Ba and not b
  3. Cb and not a
  4. Dboth a and b

Correct answer

A. neither a nor b

Step-by-step solution

We have, ⁻¹ ( a b )+ ⁻¹ ( a+b a-b )= ⁻¹ [ a b + a+b a-b 1- ( a b ) ( a+b a-b ) ]= ⁻¹ [ a²-a b+a b+b² b(a-b) b(a-b)-a(a+b) b(a-b) ]= ⁻¹ [ a²+b² a b-b²-a²-a b ]= ⁻¹ [ a²+b² - (a²+b² ) ]= ⁻¹(-1) It does not depends neither a nor b .

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