Question

find the exact value of the expression

sin 75$°$ + sin 15$°$

Short answer

sin75 $°$+sin15$°=1.2247448714$

Step-by-step solution

Step 1. Rewriting the expression 

sin(x)+sin(y)=2$\sin \left(\frac{x+y}{2}\right)\cos \left(\frac{x-y}{2}\right)$
localid="1646417268045" $$\begin{gathered} \sin 75°+\sin 15°=2\sin \left(\frac{75°+15°}{2}\right)\cos \left(\frac{75°-15°}{2}\right) \\ =2\sin 45°\cos 30° \end{gathered}$$

Step 2. Calculations

Now our expression becomes$$\begin{gathered} 2\sin 45°\cos 30°=2\frac{1}{\sqrt{2}}\frac{\sqrt{3}}{2} \\ =\sqrt{\frac{3}{2}}=1.2247448714 \end{gathered}$$