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AP EAMCET201823 Apr 2018Evening ShiftMathematicsInverse Trigonometric FunctionsActual

_ n _ r=1 ^n ⁻¹ ( 2 r r^4+r^2+2 )=

Options

  1. A4
  2. B2
  3. C- 4
  4. D- 2

Correct answer

A. 4

Step-by-step solution

Since, aligned & r^4+r^2+1= (r^2-r+1 ) (r^2+r+1 ) & So, ⁻¹ ( 2 r 1+ (r^4+r^2+1 ) ) & = ⁻¹ (r^2+r+1 )- ⁻¹ (r^2-r+1 ) & So, _ r=1 ^n ⁻¹ ( 2 r r^4+r^2+2 ) & = _ r=1 ^n ⁻¹ (r^2+r+1 )- ⁻¹ (r^2-r+1 ) & = ⁻¹ (n^2+n+1 )- ⁻¹(1) & = ⁻¹ n^2+n 1+n^2+n+1 = ⁻¹ n^2+n n^2+n+2 & So, _ n _ r=1 ^n ⁻¹ ( 2 r r^4+r^2+2 ) & = _ n ⁻¹ ( n^2+n n^2+n+2 )= 4 . aligned

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