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Question

If sec2xcosec2xdx=ktan[f(x)]+lx+C, where k,l are fixed constants and C is arbitrary constant, then which of the following is/are true

A
k+l=2
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B
The line y=kx+l passes through (5,4)
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C
f(x) is monotonically increasing function.
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D
f(x) has no stationary points
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Solution

The correct option is D f(x) has no stationary points
sec2xcosec2xdx=1cos2x1sin2xdx=sin2xcos2xdx
=tan2xdx
Now {tan2x=sec2x1}
=(sec2x1)dx
By taking terms separately, we get,
=sec2x dx1 dx
Therefore, we get
=tanxx+C
k=1, f(x)=x and l=1
k+l=0
The line y=kx+l (i.e.) y=x1 passes through (5,4)
f(x)=1>0
f(x) monotonically increases
f(x)=10
f(x) has no stationary points

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