Question

Sin 10 sin 50 sin 70 = 1/8

Answer 1

Sin 10 sin 50 sin 70 = 1/8

LHS=sin10°sin50°sin70°.

=sin10° cos(90∘−50°)cos(90∘−70°).

=2sin10∘cos10∘cos40∘cos20∘/2cos10

=2sin20∘cos20∘cos40/4 cos10

=2sin40∘cos40/8cos10∘.

=sin80/8cos10∘

=cos10/8cos10

=1/8.

Answer 2

Sin 10 sin 50 sin 70 = 1/8

LHS=sin10°sin50°sin70°.

=sin10° cos(90∘−50°)cos(90∘−70°).

=2sin10∘cos10∘cos40∘cos20∘/2cos10

=2sin20∘cos20∘cos40/4 cos10

=2sin40∘cos40/8cos10∘.

=sin80/8cos10∘

=cos10/8cos10

=1/8.