Please help me to prove (1+tan(x+z))(1+tan(y-z)) is complete square

x+y = pi/4

Given : x + y = π/4.

Let : a = (x+z) and b = (y-z).

Then : a + b = x + y = π/4.

∴ tan (a+b) = tan π/4

∴ [ ( 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

∴ tan a + tan b ( 1 + tan a ) = 1

∴( 1 + tan a ) + tan b ( 1 + tan b ) = 1 + 1

∴ ( 1 + tan a )( 1 + tan b ) = 2

∴ [ 1 + tan (x+z) ][ 1 + tan (y-z) ] = 2 .................... Ans.
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