Question

If tan a+b = 45°, prove that (1+ tan a)(1+tan b) = 2

Answer 1

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Answer 2

TAN a+b = 45°
tan a + tan b /1- tan a tan b = 1
tan a + tan b = 1- tan a tan b
tan a + tan b + tan a tan b =  1
by adding 1 on both sides we get
1+ tan a + tan b + tan a tan b =2
1(1+tan a) + tan b (1+ tan a)=2
(1+tan a) (1+tan b)=2
Hence proved