We have to prove that 1+ sin x = cos( 90 - x) + cot 45
Let's start with cos( 90 - x) + cot 45
cos (90 - x) - cot 45
cos 45 = sin 45 = 1/sqrt 2 , cos (90 - x) = sin x
=> sin x + cot 45
=> sin x + 1
which is the left hand side.
This proves that sin 45 + 1 = cos (90 - x) + cot 45.
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