Вычислите 1,5+sin^2 30°-cos^2 30°/2sin (-45°)

Так как по формуле приведения sin ( - x) = - sin (x), sin (30°) = 1/2, cos (30°) = √3/2, sin (45°) = √2/2, то:

1,5 + (sin (30°)) ^2 - (cos (30°)) ^2 / (2 * sin ( - 45°)) = 1,5 + (1/2) ^2 - (√3/2) ^2 / (2 * ( - sin (45°))) = 1,5 + 1/4 - (3/4) / (2 * ( - √2/2)) = 1,5 + 1/4 - (3/4) / ( - 2√2/2) = 3/2 + 1/4 + 3/4 / (2√2/2) = 6/4 + 1/4 + 3/4 * (2/2√2) = 7/4 + (3 * 2) / (4 * 2√2) = 7/4 + 3 / (4√2) = 7/4 + 3√2 / (4 * 2) = 14/8 + 3√2/8 = (14 + 3√2) / 8.