Question

Find the exact value of the expression-

$\cos 35°\sin 55°+\sin 35°\cos 55°$

Short answer

The required value is,

$\cos 35°\sin 55°+\sin 35°\cos 55°=$$1$

Step-by-step solution

Step 1. Given information

Given expression,

$\cos 35°\sin 55°+\sin 35°\cos 55°$

Step 2. Calculation

Solving the given expression,

$$\begin{gathered} \cos 35°\sin 55°+\sin 35°\cos 55° \\ =\cos (90°-55°)\sin 55°+\sin (90°-55°)\cos 55° \\ =\sin 55°\sin 55°+\cos 55°\cos 55° \end{gathered}$$----------$\sin \left(90°-\theta \right)=\cos \theta ,\cos \left(90°-\theta \right)=\sin \theta$

$$\begin{gathered} ={\sin }^{2}55°+{\cos }^{2}55° \\ =1 \end{gathered}$$ ----------------We know, ${\sin }^2\theta +{\cos }^2\theta =1$