Question

т75) Вычислите: (tg435° - tg375°)×sin^2(70°)×sin^2(50°)×sin^2(10°)÷sin(120°)

Спасибо!​

Answer 1

tg435=tg(360+75)=tg75°

tg375=tg15°

a)tg75-tg15=sin(75-15)/(cos75*cos15)=sin60/(sin15*cos15)==2sin60/sin30=4sin60

b)тогда (tg435-tg375)/sin120=4sin60/sin60=4

(sin120=sin60)

c)sin70*sin50=0.5(cos20-cos120)=0.5(cos20+sin30)=0.5(cos20+0.5)

d)0.5(cos20+0.5)*sin10=0.5sin10*cos20+0.25sin10=0.5*0.5(sin30+sin(-10))+

+0.25sin10=0.25(0.5-sin10)+0.25sin10=0.125=1/8

e)(tg435°-tg375°)/sin120°*sin^2(70°)*sin^2(50°)*sin^2(10°)=4*(1/8)^2=4/64=1/16