Question

Решить уравнение: tgx-sinx=2sin^2(x/2)

Answer 1

sinx/cosx -sinx=2*(1-cosx)/2
(sinx-sinxcosx)/cosx=1-cosx
sinx(1-cosx)/cosx -(1-cosx)=0
(1-cosx)(sinx-cosx)/cosx=0
cosx≠0⇒(1-cosx)(sinx-cosx)=0
1-cosx=0⇒cosx=1⇒x=2πn
sinx-cosx=0/cosx≠0
tgx-1=0⇒tgx=1⇒x=π/4+πn