Verify the identity 1+sinx=cos(90-x)+ cot45

There are 2 methods, at least to prove the
identity.

One method is to manage only the left side,
changing the value 1 into sin 90. Then, we'll transform teh sum into a
product.

The other method is to manage only the right side
and to expand the cosine of the difference.

cos (90 - x) =
cos 90*cos x + sin 90*sin x

cos 90 = 0 and sin 90 =
1

cos (90 - x) = 0*cos x + 1*sin
x

cos (90 - x) = sin x

cot 45
= 1

We'll substitute the terms from the right side and
we'll get:

1 + sin x = sin x +
1

The addition is commutative and LHS =
RHS=> the given identity,1+sinx=cos(90-x)-cot45,  is
true.