question_answer

Find the value of \[\frac{dy}{dx},\] if \[y=\cos ({{\sec }^{-1}}x+\text{cose}{{\text{c}}^{-1}}x),\] \[|x|\,\,\ge 1.\]

Answer:

we have, \[\cos ({{\sec }^{-1}}x\,+\text{cose}{{\text{c}}^{-1}}x),\] \[|x|\,\,\ge 1\] \[\Rightarrow \]   \[y=\cos \frac{\pi }{2}\] \[\left[ \because \,\,{{\sec }^{-1}}x+\text{cose}{{\text{c}}^{-1}}x=\frac{\pi }{2} \right]\] \[\Rightarrow \]   y = 0 \[\therefore \]      \[\frac{dy}{dx}=0\]