Find the value of $\sin 35°\cos 55°+\cos 35°\sin 55°$.

Find the value of the given expression.

Given expression: $\sin 35°\cos 55°+\cos 35°\sin 55°$.

$$\begin{gathered} \sin 35°\cos 55°+\cos 35°\sin 55°=\sin 35°\cos ({90}^{\circ }-35°)+\cos 35°\sin ({90}^{\circ }-35°) \\ =\sin 35°\sin 35°+\cos 35°\cos 35°[\because \cos ({90}^{\circ }-\mathrm{\theta })=\mathrm{sin\theta }\mathrm{and}\sin ({90}^{\circ }-\mathrm{\theta })=\mathrm{cos\theta }] \\ ={\sin }^{2}35°+{\cos }^{2}35° \\ =1[\because {\sin }^2\mathrm{\theta }+{\cos }^2\mathrm{\theta }=1] \\ \therefore \sin 35°\cos 55°+\cos 35°\sin 55°=1 \end{gathered}$$

Hence, the value of $\sin 35°\cos 55°+\cos 35°\sin 55°$ is $1$.