sin10+2sin25cos35=sin10+ 2*1/2 (sin(25-35)+sin(25+35))= sin10 + sin(-10) + sin 60 = sin60= √3/2

sin51cos39-sin21cos9=1/2*(sin(51-39)+sin(51+39)) - 1/2 * (sin(21-9)+sin(21+9))= 1/2 * (sin12 + sin 90) - 1/2 * (sin12 + sin30) = 1/2*sin12 + 1/2 - 1/2*sin12 - 1/2 * 1/2 = 1/2 - 1/4 = 1/4, что и требовалось доказать