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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

Consider the following two statements P and Q . P :   cos - 1 ⁡ cos ⁡ 4 π 3 = 4 π 3 Q :   sec 2 ⁡ cot - 1 ⁡ 1 2 + cosec 2 tan - 1 ⁡ 1 3 = 15 Then, which of the following is true?

Options

  1. ABoth P and Q are true
  2. BP is true, but Q is false
  3. CP is false, but Q is true
  4. DBoth P and Q are false

Correct answer

C. P is false, but Q is true

Step-by-step solution

We have, cos ⁡ 4 π 3 = - cos ⁡ π 3 = - 1 2 Hence, cos - 1 ⁡ - 1 2 = 2 π 3 Therefore, P is false. Now, sec 2 ⁡ cot - 1 ⁡ 1 2 + c o s e c 2 tan - 1 ⁡ 1 3 = 1 + tan 2 ⁡ tan - 1 ⁡ 2 + 1 + cot 2 ⁡ cot - 1 ⁡ 3 = 1 + 4 + 1 + 9 = 15 Therefore, Q is true.

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