A) 0
B) 2
C) \[-2\]
D) \[-\,4\]
E) 1
Correct Answer: D
Solution :
Given, \[y={{\sec }^{-1}}(\cos ecx)+\cos {{\sec }^{-1}}(\sec x)\] \[+{{\sin }^{-1}}(\cos x)+{{\cos }^{-1}}(\sin x)\] \[={{\sec }^{-1}}\left[ \sec \left( \frac{\pi }{2}-x \right) \right]+\cos {{\sec }^{-1}}\left[ \cos ec\left( \frac{\pi }{2}-x \right) \right]\] \[+{{\sin }^{-1}}\left[ \sin \left( \frac{\pi }{2}-x \right) \right]+{{\cos }^{-1}}\left[ \cos \left( \frac{\pi }{2}-x \right) \right]\] \[=\frac{\pi }{2}-x+\frac{\pi }{2}-x+\frac{\pi }{2}-x+\frac{\pi }{2}-x\] \[\Rightarrow \] \[y=2\pi -2x\] On differentiating w.r.t.\[x,\]we get \[\Rightarrow \] \[\frac{dy}{dx}=-4\]
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