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Manipal MET2014MathematicsInverse Trigonometric Functions

If ⁻¹ a+ ⁻¹ b+ ⁻¹ c= , then the value of a (1-a^2 ) +b (1-b^2 ) +c (1-c^2 ) will be

Options

  1. A2 a b c
  2. Ba b c
  3. C1 2 a b c
  4. D1 3 a b c

Correct answer

A. 2 a b c

Step-by-step solution

Let ⁻¹ a=A aligned ⁻¹ b & =B ⁻¹ C & =C aligned A=a, B=b, C=c aligned & and A+B+C= , then & aligned 2 A+ 2 B+ & 2 C & =4 A B C...(i) aligned aligned gathered A A+ B B+ C C =2 A B C A 1- ^2 A + B 1- ^2 B + C 1- ^2 C =2 A B C (ii) a 1-a^2 +b 1-b^2 +c 1-c^2 =2 a b c while ⁻¹ a+ ⁻¹ b+ ⁻¹ c= gathered

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