Преобразовать в произведение:

Преобразовать в сумму:

1) tga - tgb = (sin (a-b)) / (cosa*cosb)

sin (π/4 + α/2 - π/4 + α/2) / (cos (π/4 + α/2) * cos (π/4 - α/2)) = sin (α) / ((cos (π/4) * cos (α/2) - sin (π/4) * sin (α)) * (cos (π/4) * cos (α) + sin (π/4) * sin (α)) = (sinα) / (√2 (cosα - sinα) / 2) * (√2 (cosα+sina) / 2) = 2sinα / (cos^2 (α) - sin^2 (α)) = 2sina/cos (2α)

2) sinx + cosx = 2sin (x) * cos (0) = 2sinx

3) sin (5x) * sin (3x) = 0.5 * (cos (5x - 3x) - cos (5x + 3x)) = 0.5 * (cos (2x) - cos (8x)) = 0.5cos (2x) - 0.5cos (8x)

4) cos18*cos66 = 0.5 * (cos (18 - 66) + cos (18 + 66)) = 0.5 * (cos (-48) + cos (84)) = 0.5cos48 + 0.5cos84