Ineed with this question.

for the right triangle shown match the equivalent expressions.

The solution in the attached figure

Step-by-step explanation:

we know that

In the right triangle ABC

sin(A)=cos(B) and cos(A)=sin(B)

because

-------> by complementary angles

step 1

Find sin(A)

The function sine of angle A is equal to divide the opposite side angle A by the hypotenuse

substitute the values

step 2

Find sin(B)

The function sine of angle B is equal to divide the opposite side angle B by the hypotenuse

substitute the values

step 3

Find cos(A)

The function cosine of angle A is equal to divide the adjacent side angle A by the hypotenuse

substitute the values

step 4

Find cos(B)

The function cosine of angle B is equal to divide the adjacent side angle B by the hypotenuse

substitute the values

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!