Question

If x< 0 then value of tan-1(x) + tan-1 (1/x) is equal to
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Answer 1

Answer:

x<0⇒tanx<0

Let tan−1x=−t⇒x=−tant

Therefore,

−sint=1+x2x⇒−t=sin−11+x2x

Now,

x=−tant=−tan(π−t)=tan(−π+t)⇒tan−1x=−π+tan−1x⇒tan−1x=−π+cot−1x1

And 

−x=tant⇒cost=1+x21⇒t=cos−11+x21⇒−t=−cos−11+x2