Question

Oblicz. a) cos^2α-sin^2α=1-2sin^2α b)1/cosα-cosα=sinα*tgα c)1/sin^2α-1=ctg^2α Pomóżcie proszę, byłam chora i dla mnie to czarna magia.

Answer 1

a)

     cos^2(a) - sin^2(a) = 1-2sin^2(a) 

          sin^2(a) + cos^2(a) = 1

L = 1-sin^2(a) - sin^2(a) = 1-2sin^2(a)

P = 1-2sin^2(a)

L = P

 

b)

     1/cos(a) - cos(a) = sin(a) * tg(a)

L = [1-cos^2(a)]/cos(a) = [sin^2(a) + cos^2(a) - cos^2(a)]/cos(a) = sin^2(a)/cos(a) =

   = sin(a)*sin(a)/cos(a) = sin(a)*tg(a)

P = sin(a)*tg(a)

L = P 

 

c)

    1/sin^(a) -1 = ctg^2(a)

L = [1-sin^2(a)]/sin^2(a) = [sin^2(a) + cos^2(a) - sin^2(a)]/sin^2(a) = cos^2(a)/sin^2(a) =

   = ctg^2(a)

P = ctg^2(a)

L = P