perplexus.info :: Just Math : Three sins

Three sins (Posted on 2023-03-26)

Simplify, then evaluate:

sin10*sin50*sin70

P&p only.

No Solution Yet Submitted by Ady TZIDON

Rating: 4.0000 (1 votes)

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Puzzle Solution

Comment 1 of 1

Sin 10.sin50.sin70

=1/2(2 sin 10*sin50*sin70)

Now, 2 sin A* sin B = cos(A-B) -cos (A+B)

1/2(2sin10*sin 50*sin70)

=1/2(sin10(cos 20 - cos 120))

And, cos 120 = cos (90+30) = 1/2

So, 1/2(sin10*cos20)+1/4 *sin10

= 1/4(2sin10cos 20)+1/4* sin10

As 2sin Acos B = sin(A+B) - sin(A-B)

So, 1/4(sin30 - sin10) +1/4*sin10

= 1/4*sin30 -1/4*sin 10+1/4*sin10

=1/4*1/2

=1/8

Edited on March 27, 2023, 12:29 am

Posted by K Sengupta on 2023-03-26 08:30:17

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