Exact value \(\displaystyle{\sin{{\left({160}^{\circ}\right)}}}{\sin{{\left({140}^{\circ}\right)}}}{\sin{{\left({110}^{\circ}\right)}}}\)

nomadzkia0re

nomadzkia0re

Answered question

2022-04-05

Exact value sin(160)sin(140)sin(110)

Answer & Explanation

Kailee Castro

Kailee Castro

Beginner2022-04-06Added 8 answers

First use sin(180x)=sinx so:
a=sin20sin40sin70
a=sin20sin40cos20
Now use sinxcosx=sin(2x)2:
a=sin2402
and this hasn't a nice form .
Rachettolyf8

Rachettolyf8

Beginner2022-04-07Added 9 answers

I will use that: sin(a)=sin(180a),sin(a)=cos(90a) and
sin(2a)=2sin(a)cos(a)
sin(160)sin(140)sin(110)=sin(20)sin(40)sin(70)
=sin(20)sin(40)cos(20)
=sin2(40)2

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