Question

Prove that: cos10°cos30°cos50°cos70°=3/16

Answer 1

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

Hope it helps
THANK U

Answer 2

Hey dragon cos 110 can be written as cos (180-70) and we know that cos 180-theta is -cos theta so cos 110 can be written as -cos70