Question

cos 10 cos 30 cos 50 cos 70 =

Answer 1

cos10.cos30.cos50.cos70 = cos30.(cos10cos50).cos70

= √3/2 .1/2(2cos10cos50)cos70

Hint:- [ 2cosxcosy = cos(x+y) + cos(x-y) ]

= √3/2 .1/2 (cos60 + cos40 ).cos70

= √3/4 (cos60.cos70 + cos40cos70)

=√3/4 ( 1/2.cos70 + cos40cos70 )

= √3/8 ( cos70 + 2cos40cos70 )

Hint:- [ 2cosxcosy = cos(x+y) + cos(x-y) ]

= √3/8 ( cos70 + cos110 + cos30 )

Hint:- [ cos110 = cos(180-70) = - cos70

= √3/8 ( cos70 - cos70 + √3/2 )

= √3/8 . √3/2

= 3/16

Answer = 3/16