Question

[2sin50+sin10(1+根号3*tan10) ]根号（sin^280）

Answer 1

[2sin50+sin10(1+根号3*tan10) ]根号（sin^2(80))
= [2sin50+sin10(1+根号3*sin10/cos10) ] sin80
= [2sin50+sin10(1+根号3*sin10/cos10) ] cos10
= 2sin50cos10 + sin10(cos10+根号3*sin10)
= 2sin50cos10 + sin10 { 2( sin30 cos10+cos30 sin10) }
= 2sin50cos10 + sin10 { 2 sin(30+10) }
= 2sin50cos10 + 2sin10 sin40
= 2 {sin50cos10 + sin10 cos(90-40) }
= 2 {sin50cos10 + cos50sin10}
= 2 sin(50+10)
= 2sin60
=2*根号3/2
= 根号3

Answer 2

解：
原式=[ 2sin50°+sin10°(1＋√3·tan10°)]√2cos10°
=2√2sin50°cos10°+√2 sin10°cos10°+√6 sin^210°
=2√2sin50°cos10°+√2/2 sin20°+√6/2(1-cos20°)
=2√2sin50°cos10°+√2/2 sin20°-√6/2cos20°+√6/2
=2√2sin50°cos10°-√2(√3/2cos20°-1/2sin20°)+√6/2
=2√2sin50°cos10°-√2sin(60°-20°)+√6/2
=2√2sin50°cos10°-√2sin40°+√6/2
=2√2sin50°cos10°-√2sin(50°-10°)+√6/2
=2√2sin50°cos10°-√2sin50°cos10°+√2cos50°sin10°+√6/2
=√2sin50°cos10°+√2cos50°sin10°+√6/2
=√2sin60°+√6/2
=√6

追问

是根号（sin^280），不是根号（2sin^280）