If sin-1 x + sin-1 y = \(\rm \frac{3\pi}{4}\) , then cos-1 x + cos-1 y = ? . 

  1. -3π/4
  2. π/4 
  3. -π/4
  4. 3π/2 

Answer (Detailed Solution Below)

Option 2 : π/4 
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Detailed Solution

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Concept:

sin-1 x + cos-1 x = \(\rm \frac{π}{2}\)  

Calculation:

sin-1 x + sin-1 y = \(\rm \frac{3π}{4}\) 

⇒ \(\rm \left ( \frac{π}{2} -cos^{-1}x\right ) + \left ( \frac{π}{2}- cos^{-1}y\right ) = \frac{3π}{4}\) 

⇒ π - ( cos-1 x + cos-1 y ) = \(\rm \frac{3π}{4}\)

cos-1 x + cos-1 y = \(\rm\frac{\pi}{4}\) 

The correct option is 2.

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