Expand tre pollowing \( ? \) simplify where possible \( 11 \cos \left(6+80^{\circ}\right) \) \( 2 \cdot \sin \left(660^{\circ}\right) \)

We are asked to “expand” and simplify the two expressions:   1) 11·cos(6 + 80°)   2) 2·sin(660°) Before proceeding, note that we assume the angle measures are in degrees. (In expression 1 the number 6 is written without a degree symbol, but since 80° is given, we interpret 6 as 6° so that the whole angle is 6° + 80°.) ────────────────────────────── Step 1. Expand 11·cos(6° + 80°) Recall the cosine angle‐sum formula:   cos(A + B) = cos A · cos B – sin A · sin B Letting A = 6° and B = 80° we have:   cos(6° + 80°) = cos6° · cos80° – sin6° · sin80° Thus, multiplying by 11 gives:   11·cos(6° + 80°) = 11·[cos6° · cos80° – sin6° · sin80°] This is the expanded form. ────────────────────────────── Step 2. Simplify 2·sin(660°) First, note that the sine function is periodic with period 360°. Therefore, we can reduce the angle:   660° − 360° = 300° Thus, sin(660°) = sin(300°). Now recall that 300° is in the fourth quadrant, where sine is negative. We also know:   sin(300°) = –sin(60°) and   sin(60°) = √3⁄2. Therefore:   sin(300°) = –(√3⁄2). Multiplying by 2 we have:   2·sin(660°) = 2·sin(300°) = 2·[–(√3⁄2)] = –√3. ────────────────────────────── Final Answers: 1) 11·cos(6° + 80°) = 11[cos6° · cos80° – sin6° · sin80°] 2) 2·sin(660°) = –√3