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Question

In ΔABC with the length of sides as a,b,c, if tan1(bc+a)+tan1(ca+b)=π4 and a+b+c=2s, then its area is

A
s(sa)
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B
s(sb)
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C
s(sc)
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D
s2
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Solution

The correct option is A s(sa)
tan1(bc+a)+tan1(ca+b)=π4

tan1⎢ ⎢ ⎢ ⎢bc+a+ca+b1(bc+a)(ca+b)⎥ ⎥ ⎥ ⎥=π4

b(a+b)+c(c+a)(c+a)(a+b)bc=tanπ4=1

ab+b2+c2+ca=ca+bc+a2+abbc
b2+c2=a2
A=90

We know that cotA2=s(sa)Δ
cot45=s(sa)Δ
Δ=s(sa)

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