Maths · Inverse trigonometrical functions and their properties
If value of which satisfy equation ^{2}-3\left(\cot ^{-1} x\right)+2>0 \) is or
If value of \( \mathbf{x} \) which satisfy equation \( \left(\cot ^{-1} x\right)^{2}-3\left(\cot ^{-1} x\right)+2>0 \) is \( x< \) \( \cot a \) or \( x>\cot b \) Find the value of \( a+b \)
- A. 1
- B. 2
- C. 3 \)
- D. 4
Step-by-step solution
Let y = cot⁻¹x. Then inequality becomes y² - 3y + 2 > 0 ⇒ (y-1)(y-2) > 0 ⇒ y < 1 or y > 2. Since cot⁻¹x is decreasing on (0,π), y < 1 ⇒ x > cot1, and y > 2 ⇒ x < cot2. Thus a = 2, b = 1, so a+b = 3.
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