Given the right triangle ABC, where A=90 degrees, calculate the expression: E=cosB/sinC+ cosC/sinB

We'll calculate the first ratio:
cosB/sinC

We know that A = pi/2 and the sum of the angles
of a triangle is pi.

A + B + C =
PI

pi/2 + B + C = pi

B + C =
pi - pi/2

B  +C = pi/2

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

Now, we'll calculate the second
ratio:

 cosC/sinB = cos (pi/2 - B)/sin
B

 cosC/sinB = sin B/sin
B

 cosC/sinB = 1

The value of
the given expression is:

E = 1 +
1

E =
2