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Question

If y=esin1(t21) and x=esec1(1t21) then dydx is equal to

A
xy
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B
yx
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C
yx
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D
xy
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Solution

The correct option is B yx
We have, y=esin1(t21) and x=esec1(1t21)=ecos1(t21), [cos1x=sec11x]
Now multiply x and y,
xy=esin1(t21)ecos1(t21)=esin1(t21)+cos1(t21)=eπ/2 [sin1θ+cos1θ=π2]
xy=constant
Differentiate both sides w.r.t. x
y+xydx=0
dydx=yx

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