prove that sin 20*sin40+sin60*sin80=3/16 how does it comes

Question

Arun · Answer

since,sin60= √ 3 /2 = √ 3 /2( sin20sin40sin80) = √ 3 /2( sin20sin80sin40) = √ 3 /4 [(2sin20sin40)sin80] on applying [cos(A-B)-cos(A+B) = 2sinAsinB] we get, = √ 3 /4 (cos20-cos60)sin80 [since,cos(-a)=cosa] = √ 3 /4(cos20sin80-cos60sin80) = √ 3 /8(2sin80cos20-sin80) = √ 3 /8(sin100+sin60-sin80) = √ 3/8( √ 3/2+sin100-sin80 ) = √ 3/8( √ 3/2+sin(180-80)-sin80 ) = √ 3/8( √ 3/2+sin80-sin80 ) [since,sin(180-a)=sina] = √ 3/8( √ 3/2) = 3/16

Chinmay sambhe · Answer

Since sin 60= root3/2 => root3/2 [ sin 20 . Sin 40 . Sin 80] => root3/2 [ sin 20 . Sin (60-20) . Sin (60+ 20) ] We know that sin x . Sin (60-x) . Sin (60+ x) = ¼ sin 3x Therefore, root3/2 [ ¼ sin60] Root 3/2 . ¼ . root 3/2 => 3/16.

Rishi Sharma · Answer

Hello student,
The problem posted by you needs a small correction, it should be
sin20 * sin40 * sin60 * sin80 = 3/16
I hope the attached solution image will solve your doubts.
Thank You
All the best for your exams.
645-1163_WhatsApp Image 2020-06-04 at 8.11.48 PM(1).jpeg

645-1163_WhatsApp Image 2020-06-04 at 8.11.48 PM(1).jpeg

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prove that sin 20sin40+sin60sin80=3/16 how does it comes

prove that sin 20sin40+sin60sin80=3/16
how does it comes

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