prove that cos 10 cos30 cos50 cos70 = 3/16 - Maths - Trigonometric Functions

Question

prove that cos 10 cos30 cos50 cos70 = 3/16

Pia Vanave · Accepted Answer

cos30 (cos50cos10) cos70
= root3/2 1/2(2cos10cos50)cos70
= root3/2 1/2 (cos60 + cos40 ) cos70 [ bcoz 2cosxcosy =
cos(x+y) + cos(x-y) ]
= root3/4 (cos60 cos70 + cos40cos70)
= root3/8 [ cos70 + 2cos40cos70 ]
= root3/8 [ cos70 + cos110 + cos30 ]
= root3/8 [ cos70 - cos70 + root3/2]
= root3/8 root3/2
= 3/16

prove that cos 10.cos30.cos50.cos70 = 3/16