Question

16 sino coso cos20 cos40 cos80 = sin 160​

Answer 1

Answer:

10 °

Step-by-step explanation:

2sin x cos x = sin 2x

16 sin o cos o cos 20 cos80 cos 80  = sin160

here sin160 can be written as ,

sin160 = 2 sin80cos80 =2 *2 (sin40 cos40)cos80

          = 2*2*2 ((sin20 cos20) cos 40) cos80

          = 2 *2*2*2 ((sin10cos10)cos 20 cos40 cos 80

∴ 16 sin o cos o cos 20 cos80 cos 80 = 16 ((sin10cos10)cos 20 cos40 cos 80

16 sin o cos o cos 20 cos80 cos 80 = 16 ((sin10cos10)cos 20 cos40 cos 80

⇒ sin o cos o   = sin 10 cos 10

   sin 2o = sin20

o = 10 °