AMO 2027 Grades 10-12 SET 1 - Self-study Question 9

Find the value of $$X=\cos(57^\circ)\cos(27^\circ)+\sin(57^\circ)\sin(27^\circ),$$ if $\cos(57^\circ)=0.5446$, $\cos(27^\circ)=0.8910$, and all values inside sine and cosine are in degrees.

**Editorial clarification.** Treat the printed decimal cosine values as rounded approximations. Use the stated angles exactly.

Choose one option.