Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of the expression. cot25^{circ}\cdot csc65^{circ}\cdot sin25^{circ}

We can use the Fundamental Identities to simplify the expression: $$cot25^{circ}=frac{cos25^{circ}}{sin25^{circ}}$$ $$csc65^{circ}=frac{1}{sin65^{circ}}$$ Substituting these expressions into the given expression, we get: $$cot25^{circ}cdotcsc65^{circ}cdotsin25^{circ}=frac{cos25^{circ}}{sin25^{circ}}cdotfrac{1}{sin65^{circ}}cdotsin25^{circ}$$ Using the Complementary Angle Theorem, we know that: $$cos25^{circ}=sin(90^{circ}-25^{circ})=sin65^{circ}$$ Substituting this into our expression, we get: $$frac{cos25^{circ}}{sin25^{circ}}cdotfrac{1}{sin65^{circ}}cdotsin25^{circ}=frac{sin65^{circ}}{sin65^{circ}}cdotfrac{sin25^{circ}}{sin25^{circ}}cdotfrac{1}{sin65^{circ}}=frac{1}{sin65^{circ}}$$ Therefore, the exact value of the expression is: $$boxed{frac{1}{sin65^{circ}}}$$