Question

express the following as sum or difference of trigonometric ratios
2cos 54°.sin 66°​

Answer 1

We know that,

$\sf{2\ \cos x\ \sin y=\sin (x+y)-\sin (x-y)}$

Then,

$\sf{2\cos 54^{\circ}\sin 66^{\circ}=\sin (54^{\circ}+66^{\circ})-\sin (54^{\circ}-66^{\circ})}\\\\\\\sf{2\cos 54^{\circ}\sin 66^{\circ}=\sin 120^{\circ}-\sin (-12^{\circ})}\\\\\\\underline {\underline {\sf{2\cos 54^{\circ}\sin 66^{\circ}=\sin 120^{\circ}+\sin 12^{\circ}}}}$