Преобразовать в произведение:
[tex]1)tg( \frac{ \pi }{4} + \frac{ \alpha }{2})-tg( \frac{ \pi }{4} - \frac{ \alpha }{2})[/tex]
[tex]2)sinx+cosx[/tex]
Преобразовать в сумму:
[tex]1)sin5x*sin3x[/tex]
[tex]2)cos18*cos66[/tex]

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) = 2sinx3) 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