Question

cos pi/12 sin pi/8 cos pi/8


urgent ofer 55 de puncte

Answer 1

Răspuns:

cos π/12=(√6+√2)/4

sinπ/8=1/2*√(2-√2)

cosπ/8=1/2*√(2+√2)

Explicație pas cu pas:

cos(x-y)=cosx*cosy+sinx*siny

cos π/12=cos(π/4- π/6)

=cos π/4*cos π/6+sin π/4*sin π/6

=√2/2*√3/2+√2/2*1/2

cos π/12=(√6+√2)/4

cos²x/2=(1+cosx)/2 ;  sin²x=(1-cosx)/2

π/8=( π/4)/2

sin²π/8=(1-cosπ/4)/2=(1-√2/2)/2=(2-√2)/4

sinπ/8=√[(2-√2)/4]

sinπ/8=1/2*√(2-√2)

cos²π/8=(1+cosπ/4)/2 =(1+√2/2)/2=(2+√2)/4

cosπ/8=√[(2+√2)/4]

cosπ/8=1/2*√(2+√2)