Question

sprawdz tożsamości:

a)(sin alpha +cos alpha )^{2} + (sin apha -cos alpha )^2=2

b)(tg alpha-1)(ctg alpha+1)=tg alpha-ctg alpha

c)1+ctg a;pha = sin apha +cos apa : sin alpha

Answer 1

alfa = x

si^2 x + cos^2 x = 1

tgx * ctgx = 1

a)

(sinx + cosx)^2 +(sinx - cosx)^2 = 2

L = sn^2 x + 2sinx cosx + cos^2 x + sin^2 x - 2sinxcosx + cos^2 x = 1+1 = 2

L = P

b)

(tgx -1)(ctgx +1) = tgx - ctgx

L = tgx * ctgx + tgx - ctgx -1 = 1 + tgx - ctgx -1 = tgx - ctgx

L = P

c)

1 + ctgx =(sinx + cosx)/sinx

P = (sinx + cosx)/sinx = sinx/sinx + cosx/sinx = 1 + ctgx

P = L