1.[tex] \frac{tgx+tgy}{tg(x+y)}+ \frac{tgx-tgy}{tg(x-y)}= [/tex]
2.[tex]sin(\pi-2 \alpha )+2cos( \frac{3}{2}\pi+ \alpha )sin( \frac{3}{2}\pi- \alpha )= [/tex]
3.[tex]cos^{4} \frac{ \alpha }{2}-sin^{4} \frac{ \alpha }{2} [/tex]
2.[tex]sin(\pi-2 \alpha )+2cos( \frac{3}{2}\pi+ \alpha )sin( \frac{3}{2}\pi- \alpha )= [/tex]
3.[tex]cos^{4} \frac{ \alpha }{2}-sin^{4} \frac{ \alpha }{2} [/tex]
Answers & Comments
tg (a - b) = (tg a - tg b) / (1 + tg a tg b)
(tg x + tg y)/tg(x + y) + (tg x - tg y) / (tg(x-y) = (tg x + tg y) / (tg x + tg y) * (1 - tg x tg y) + +(tg x - tg y) / (tg x - tg y) * (1 + tg x tg y) = 1 - tg x tg y + 1 + tg x tg y = 2
2. sin (π - 2a) + 2 cos(3/2π + a)sin(3/2π-a) = sin 2a + 2 sin a (-cos a) = 2 sin a * cos a - 2 sin a cos a = 0
3. cos^4 a/2 - sin^4 a/2 = (cos ² a - sin ²a)(cos² a + sin² a) = cos²a - sin²a = cos 2a