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

| Certified Educator

We have a right triangle with A = 90 degrees and we have to calculate cos B / sin C + cos C / sin B

Let's take the sides opposite angle A as a, that opposite angle B as b and that opposite angle C as c.

cos B / sin C + cos C / sin B

=> [(c / a)/(c/ a)] + [(b/a)/(b/a)]

=> 1 + 1

=> 2

The expression = 2.

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giorgiana1976 | Student

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