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JEE Main20268 April 2026Evening ShiftMathematicsInverse Trigonometric FunctionsActual

Let = 3 ⁻¹ ( 6 11 ) and = 3 ⁻¹ ( 4 9 ) , where inverse trigonometric functions take only the principal values. Given below are two statements: Statement I: ( + ) > 0 . Statement II: ( ) In the light of the above statements, choose the correct answer from the options given below:

Options

  1. ABoth Statement I and Statement II are true
  2. BBoth Statement I and Statement II are false
  3. CStatement I is true but Statement II is false
  4. DStatement I is false but Statement II is true

Correct answer

A. Both Statement I and Statement II are true

Step-by-step solution

We are given = 3 ⁻¹ ( 6 11 ) and = 3 ⁻¹ ( 4 9 ) . First, we find the range of . Since 1 2 6 Multiplying by 3 , we get 2 Since lies in the second quadrant, ( ) Next, we find the range of . Since 0 3 Multiplying by 3 , we get Thus, lies in the third quadrant. Now, we determine the sign of ( + ) . Adding the inequalities for and : 2 + 3 2 The angle ( + ) lies in the interval ( 3 2 , 9 4 ) , which covers the fourth quadrant and a part of the first quadrant. In both of these regions, the cosine function is strictly posi

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