1observe
its tan-11+tan-1(√1-x2/√1+x2).
Q1) y=tan-1[√1+x2 + √1-x2 /√1+x2 - √1-x2], then dy/dx=?
a) 1/√1-x4
b) -1/√1-x4
c) x/√1-x4
d) -x/√1-x4
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2 Answers
1Answer is d
first of all rationalize stuff inside the tan inverse function.
this will get you tan-1(1+√1-x4x2)
now assume cos2z = x
By applying trigonometry now, you may reach
tan-1 ( 1+tanz1-tanz)
which is equal to tan-1(tan 45 + z)
which is equal to 45 degrees + z
now put z = cos-1x22
differentiating now.....we get d as the answer