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MHT CET202311 May 2023Morning ShiftMathematicsInverse Trigonometric FunctionsActual

If =3 ⁻¹ 6 11 and =3 ⁻¹ ( 4 9 ) , where the inverse trigonometric functions take only the principal values, then the incorrect option is

Options

  1. A>0
  2. B< 0
  3. C( + )>0
  4. D< 0

Correct answer

A. >0

Step-by-step solution

=3 ⁻¹ 6 11 and =3 ⁻¹ ( 4 9 ) Since 6 11 > 6 12 Taking ⁻¹ on both sides, we get ⁻¹ ( 6 11 )> ⁻¹ ( 6 12 ) [ ⁻¹ x . is an increasing function ] 3 ⁻¹ ( 6 11 )>3 ⁻¹ ( 1 2 ) >3 ( 6 ) > 2 Now, 4 9 ⁻¹ ( 4 8 ) [ ⁻¹ x . is a decreasing function ] 3 ⁻¹ ( 4 9 )>3 ⁻¹ ( 1 2 ) >3 ( 3 ) > From (i) and (ii), we have lies in II ^ nd quadrant and lies in III ^ rd quadrant. 2 + ....[From (i) and (ii)] + > 3 2 Thus, + lies in IV ^ th quadrant. So, ( + )>0 [Note: Options (B), (C) and (D) are correct.]

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