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Question

If x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals
(a) π2

(b) -π2

(c) − π

(d) none of these

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Solution

(b) -π2
We know that tan-1x+tan-1y=tan-1x+y1-xy.
x<0, y<0 such that
xy=1

Let x = -a and y = -b, where a and b both are positive.

tan-1x+tan-1y=tan-1x+y1-xy=tan-1-a-a1-1=tan-1-=tan-1tan-π2=-π2

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