Question

Sin2A*cosA/(1+cos2A)*(1+cosA)=

Answer 1

Sin2α*Сosα/(1+Сos2α)*(1+Сosα )=?
числитель = Sin2α*Сosα = 2SinαCosαCosα = 2SinαCos²α
знаменатель = (1+Сos2α)*(1+Сosα) = (1 + Сos²α -Sin²α)(1 + Cosα) =
= 2Cos²α(1 +Cosα)
видим, что дробь можно сократить на 2Cos²α
и теперь пример:
Sinα/(1 +Cosα)= tgα/2

Answer 2

We can start by simplifying the expression using trigonometric identities:

sin2A = 2sinA*cosA (double angle identity) cos2A = cos^2A - sin^2A = 1 - 2sin^2A (double angle identity)

Substituting these identities into the expression, we get:

(2sinAcosAcosA) / (1 + (1 - 2sin^2A))*(1 + cosA)

Simplifying further:

(2sinAcosAcosA) / (2 - 2sin^2A)*(1 + cosA)

Canceling out the common factor of 2:

(sinAcosAcosA) / (1 - sin^2A)*(1 + cosA)

Using the identity cos^2A = 1 - sin^2A:

(sinAcosAcosA) / (cos^2A)*(1 + cosA)

Canceling out the common factor of cosA:

sinA*cosA / (1 + cosA)

This is the simplified form of the expression.