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Prove that (1+tanA)(1+tanB)=2 if A+B=45°

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Given A+B=45degree
Rightarrow an (A+B)=1
Rightarrow frac( an A+ an B)(1- an A* an B)=1
Taking the denominator to the R.H.S. and rearranging the factor,we get
Rightarrow an A+ an B+ an A* an B=1
Adding 1 on both sides,we get
Rightarrow 1+ an A+ an B+ an A* an B=1+1
Rightarrow 1(1+ an A)+ an B(1+ an A)=2
Rightarrow (1+ an A)(1+ an B)=2
HENCE PROVED.

Posted by

Deependra Verma

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