Question

пожалуйста помогите решить уравнение(тождество) cos(p/4+x)-cos(p/4-x)=1

Answer 1

cos(p/4+x)-cos(p/4-x)=1

cos(p/4+x) = cospi/4*cosx - sinx*sinpi/4 = √2/2(cosx-sinx)

cos(p/4-x) = cospi/4*cosx + sinx*sinpi/4 =√2/2(cosx+sinx)

cos(p/4+x)-cos(p/4-x) = √2/2(cosx-sinx) - (√2/2(cosx+sinx)) = √2/2(cosx-sinx-cosx-sinx) = -√2/2 * sinx = -√2sinx

cos(p/4+x)-cos(p/4-x)=1   =>

-√2sinx =1

sinx= - √2/2

x=((-1)^(k+1))  *pi/4+pi*k