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COMEDK2023Evening ShiftMathematicsInverse Trigonometric FunctionsActual

The value of ⁻¹ [ (39 5 ) ] is

Options

  1. A2
  2. B3 5
  3. C-3 10
  4. D3 10

Correct answer

D. 3 10

Step-by-step solution

The given expression is ⁻¹ [ (39 5 ) ] . First, simplify the angle 39 5 by dividing by 2 : 39 5 = 7 + 4 5 = 8 - 5 . Using the periodicity of the cosine function, (8 - ) = ( ) , so: (39 5 ) = (- 5 ) = ( 5 ) . Now, rewrite the cosine term as a sine term using the identity ( ) = ( 2 - ) : ( 5 ) = ( 2 - 5 ) = ( 5 - 2 10 ) = ( 3 10 ) . Substituting this back into the original expression: ⁻¹ [ ( 3 10 ) ] . Since 3 10 lies within the principal value range of ⁻¹(x) , which is [- 2 , 2 ] , the expression simplifies to 3 10

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