Question

Тригонометрия. помогите решить

Answer 1

tgβ=1/5, sin2β - ?
1+tg²β=1/cos²β
1+(1/5)²=1/cos²β
1+1/25=1/cos²β
26/25=1/cos²β
cos²β=25/26, cosβ=√(25/26)
sin²β+cos²β=1
sin²β+25/26=1
sin²β=1/26
sinβ=√(1/26)
sin2β=2sinβ*cosβ
sin2β=2*√(1/26)*√(25/26)=2*√(25/26²)=2*(5/26)=5/13