Question

1) cos70° + cos50° 2) cos70° + cos10° 3) sin48° + sin12°

Answer 1

Cosa+cosb=2cos(a+b)/2cos(a-b)/2
Cos50+cos70=2cos(50+70)/2cos(50-70)/2=2cos60cos10=2*1/2cos10=cos10
Второй тоже
Cos10+cos70=2cos40cos30=2*sqrt(3)/2cos40=sqrt(3)cos40
Sina+sinb=2sin(a+b)/2cos(a-b)/2
Sin48+sin12=2sin30cos18=2*1/2cos18=cos18

Answer 2

1. Using the sum-to-product identity for cosine, we have:

cos 70° + cos 50° = 2 cos((70°+50°)/2) cos((70°-50°)/2) = 2 cos 60° cos 10° = 1 cos 10° = cos 10°

Therefore, cos 70° + cos 50° = cos 10°.

2. Again using the sum-to-product identity for cosine, we have:

cos 70° + cos 10° = 2 cos((70°+10°)/2) cos((70°-10°)/2) = 2 cos 40° cos 30° = sqrt(3) cos 40°

Therefore, cos 70° + cos 10° = sqrt(3) cos 40°.

3. Using the sum-to-product identity for sine, we have:

sin 48° + sin 12° = 2 sin((48°+12°)/2) cos((48°-12°)/2) = 2 sin 30° cos 18° = sqrt(3) cos 18°

Therefore, sin 48° + sin 12° = sqrt(3) cos 18°.