Find the value of cos 9°+sin 9°.

\(\sqrt {2}\)sin 54°

Divide & Multiply the eq. by \(\sqrt{2}\)

\(\frac{\sqrt{2}}{\sqrt{2}}\) (cos 9°+sin 9°)

Sin(A+B) = sinA cosB + cosAsinB

\(\sqrt{2}\left(\frac{1}{\sqrt{2}} \cos 9^{\circ}+\frac{1}{\sqrt{2}} \sin 9^{\circ}\right) \)

\(\sqrt{2}\left(\sin 45^{\circ} \cos 9^{\circ}+\cos 45^{\circ} \sin 9^{\circ}\right) \)

\(\sqrt{2}(\sin (45+9)) \)

\(\sqrt{2} \sin 54^{\circ}\)