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Question

If y(x)=cot1(1+sinx+1sinx1+sinx1sinx), x(π2,π), then dydx at x=5π6 is

A
12
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B
1
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C
12
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D
0
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Solution

The correct option is C 12
1+sinx=sinx2+cosx2 and 1sinx=sinx2cosx2

y(x)=cot1⎜ ⎜2sinx22cosx2⎟ ⎟=cot1(tanx2)=π2x2
dydx=12

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