Find the exact value of the expression. Do not use a calculator. cos(-(17pi )/(4))-csc(-(17pi )/(4)) Select the correct choice below and, if necessary.fill in the answer box to complete your choice. A. cos(-(17pi )/(4))-csc(-(17pi )/(4))= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. B. The answer is undefined.

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Answer 1

To find the exact value of the expression, we need to simplify the trigonometric functions.The cosine function is an even function, which means that

. Therefore, we can rewrite the expression as:

Next, let's simplify the cosecant function. The cosecant function is the reciprocal of the sine function, so

. Also, the sine function is an odd function, which means that

. Therefore, we can rewrite the expression as:

Now, let's simplify the sine function. The sine function has a period of

, which means that

for any integer

. Therefore, we can rewrite the expression as:

To find the exact value of the expression, we need to find the value of

modulo

. Since

is greater than

, we can subtract

until we get a value less than

. We get:

Therefore, we can rewrite the expression as:

The exact values of the cosine and sine functions for

are

and

, respectively. Therefore, we can substitute these values into the expression:

Simplifying further, we get:

Rationalizing the denominator, we get:

Simplifying further, we get:

Therefore, the exact value of the expression is

.So, the correct choice is A.

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