Given sin x + cos x = 1, what is tan(x+x)?

Expert Answers

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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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