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AP EAMCET201923 Apr 2019Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If (- 2 < < 2 ), then ( ( ( 4 + 2 ) )= )

Options

  1. A( ⁻¹ ( 2 ) )
  2. B(2 ⁻¹ ( 2 ) )
  3. C( coth ⁻¹ ( 2 ) )
  4. D(2 coth ⁻¹ ( 2 ) )

Correct answer

B. (2 ⁻¹ ( 2 ) )

Step-by-step solution

( array rlrl Let & ( ( 4 + 2 ) ) =x & ( 4 + 2 ) =e^x & 1+ 2 1- 2 =e^x array ) On applying componendo and dividendo rule, we get ( aligned 2 & 2 2 2 = e^x-1 e^x+1 & 2 = e^ x / 2 -e^ -x / 2 e^ x / 2 +e^ -x / 2 = ( x 2 ) & x 2 = ⁻¹ ( 2 ) & x =2 ⁻¹ ( 2 ) aligned ) Hence, option (b) is correct.

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