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

Answers (1)

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.

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