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Question

Differentiate tan11+x21x w.r.t. tan1x.

A
12
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B
12
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C
14
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D
14
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Solution

The correct option is A 12
Let y=tan11+x21x and
z=tan1xx=tanz, Now we have to find dydz.
y=tan11+tan2z1tanz=tan11coszsinz=tan12sin2(z2)2sin(z2).cos(z2)
=tan1tan(z2)y=12z.
dydz=12.

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