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.

To find the exact value of the expression, we need to simplify the trigonometric functions.<br /><br />The cosine function is an even function, which means that $cos(-x) = cos(x)$. Therefore, we can rewrite the expression as:<br /><br />$cos(-\frac {17\pi }{4})-csc(-\frac {17\pi }{4}) = cos(\frac {17\pi }{4})-csc(-\frac {17\pi }{4})$<br /><br />Next, let's simplify the cosecant function. The cosecant function is the reciprocal of the sine function, so $csc(x) = \frac{1}{sin(x)}$. Also, the sine function is an odd function, which means that $sin(-x) = -sin(x)$. Therefore, we can rewrite the expression as:<br /><br />$cos(\frac {17\pi }{4})-\frac{1}{sin(-\frac {17\pi }{4})}$<br /><br />Now, let's simplify the sine function. The sine function has a period of $2\pi$, which means that $sin(x) = sin(x + 2k\pi)$ for any integer $k$. Therefore, we can rewrite the expression as:<br /><br />$cos(\frac {17\pi }{4})-\frac{1}{sin(\frac {17\pi }{4} + 2k\pi)}$<br /><br />To find the exact value of the expression, we need to find the value of $\frac {17\pi }{4}$ modulo $2\pi$. Since $\frac {17\pi }{4}$ is greater than $4\pi$, we can subtract $4\pi$ until we get a value less than $2\pi$. We get:<br /><br />$\frac {17\pi }{4} - 4\pi = \frac {17\pi }{4} - \frac {16\pi }{4} = \frac {\pi }{4}$<br /><br />Therefore, we can rewrite the expression as:<br /><br />$cos(\frac {\pi }{4})-\frac{1}{sin(\frac {\pi }{4})}$<br /><br />The exact values of the cosine and sine functions for $\frac {\pi }{4}$ are $\frac {\sqrt {2}}{2}$ and $\frac {\sqrt {2}}{2}$, respectively. Therefore, we can substitute these values into the expression:<br /><br />$\frac {\sqrt {2}}{2}-\frac{1}{\frac {\sqrt {2}}{2}}$<br /><br />Simplifying further, we get:<br /><br />$\frac {\sqrt {2}}{2}-\frac {2}{\sqrt {2}}$<br /><br />Rationalizing the denominator, we get:<br /><br />$\frac {\sqrt {2}}{2}-\frac {2\sqrt {2}}{2}$<br /><br />Simplifying further, we get:<br /><br />$\frac {\sqrt {2}}{2}-\sqrt {2}$<br /><br />Therefore, the exact value of the expression is $\frac {\sqrt {2}}{2}-\sqrt {2}$.<br /><br />So, the correct choice is A.