The given expression is:
![\sin (-t)-\sin t](https://img.qammunity.org/2023/formulas/mathematics/high-school/bbyvkqqpxtt85befcq60zlr49ncyyjnmwd.png)
Recall the definition of an odd function:
![f(-x)=-f(x)](https://img.qammunity.org/2023/formulas/mathematics/high-school/2e7atz772vwog13fsb2sz63eyu41ii9qrs.png)
Since the sine function is an odd function, it follows that:
![\sin (-t)=-\sin t](https://img.qammunity.org/2023/formulas/mathematics/high-school/cyia4dn9w1jznpr4m4nig33gbiqsyfmr3u.png)
Substitute this into the given expression:
![\sin (-t)-\sin t=-\sin t-\sin t](https://img.qammunity.org/2023/formulas/mathematics/high-school/2mmkqm0wbba6h7h4u5l5v9yfltqp2oa2o9.png)
Simplify the expression:
![-2\sin t](https://img.qammunity.org/2023/formulas/mathematics/high-school/m2yuic26c9a1bourt6swtfgqykpbf3myw6.png)
Substitute sin t =a into the expression:
![\begin{gathered} -2(a) \\ =-2a \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/sr5a4htnf761clt47mqvxqb2hcgansju1e.png)
Hence, the expression in terms of a is -2a.
The answer is -2a.