Question

If(a+b)=45 find the value of (1+tan A) (1+tan B)

Answer 1

A+B= 45
Tan(a+b)= tan 45 = 1
also.
tan (a+b)= tan a + tan b/1-tan a tan b
so..

1= tan a +tan b/1-tan a tan b
1-tan a tan b= tan a + tan b
so. 1= tan a + tan b +tan a tan b
so. tan a + (1+tan a) tan b =1
adding 1 on both side
1+tan a +(1+tan a) tan b = 2
(1+tan a)(1+tan b)= 2

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Answer 2

Taking L.H.S
tan (A+B)=tan A+tanB/1-tanAtanB
=tan45=tanA+tanB/1-tanAtanB
=1-tanAtanB=tanA+tanB
=2=1+tanA+tanB+tanAtanB
=2=(1+tanA)(1+tanB)
Hence Proved