Verify if the identity is true? cosC/sin(90-C)-1=1-cosB/sin(90-B)

We'll re-write the identity, shifting it's
terms:

cosC/sin(90-C) + cosB/sin(90-B) =
1+1

cosC/sin(90-C) + cosB/sin(90-B) =
2

We'll calculate the first ratio:
cosB/sinC

We know that in a right angle triangle, we'll have the
identities:

B = pi/2 - C

Now, we'll
apply cosine function both sideS:

cos B = cos (pi/2 -
C)

cos B = cos pi/2*cos C + sin pi/2*sin
C

cos pi/2 = 0 and sin pi/2 =1

cos B =
sin C

cosB/sinC = sin C/sin C = 1

We'll
apply the same identities for the other fraction:

cosC/sinB = cos
(90 - B)/sin B

cosC/sinB = sin B/sin
B

cosC/sinB = 1

Managing the left side,
we'll get:

LHS = 1 + 1 = 2 =
RHS

We notice that we've get the same result both
sides, so the identity cosC/sin(90-C)-1=1-cosB/sin(90-B) is
true.