We have to find tan(x + x), given that sin x + cos x = 1.
We know that (sin x)^2 + (cos x)^2 = 1
sin x + cos x = 1
=> (sin x + cos x)^2 = 1
=> (sin x)^2 + (cos x)^2 + 2 sin x cos x = 1
=> 1 + 2 sin x cos x = 1
=> 2 sin x cos x = 0
=> sin 2x = 0
Now tan (x +x) = tan 2x = sin 2x / cos 2x
as sin 2x = 0
tan 2x = sin 2x/ cos 2x = tan (x +x) = 0
Therefore we prove that tan (x +x) = 0
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