3 years ago

1/2+1/3 ———— 1/4-1/5

Mathematics

2 answers:

leva [86]3 years ago

5 0

I got 50/60 divided by 3/60 but i dont know how to do the rest. Hope this helps

olga_2 [115]3 years ago

4 0

Top:1/2+1/3=2/6
Bottom:5/20-4/20=1/20

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Prove that sin20sin40sin60sin80=3/16

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We'll use the following properties of sine and cosine to prove this:

$sin(a)\cdot sin(b) = \frac12(cos(a-b) - cos(a+b))$

$cos(a)\cdot cos(b) = \frac12(cos(a+b) + cos(a-b))$

$cos(180+a) = cos(180-a)$

Then it's just a matter of filling it in...

sin20sin40 * sin60sin80 = 1/2(cos20 - cos60) * 1/2 (cos20 - cos140) =

1/8( cos40 + 1 - cos160 - cos120 - cos40 - cos80 + cos80 + cos200) =

1/8(1 - cos160 - cos120 + cos200) =

1/8(1 - cos160 - cos120 + cos160) =

1/8(1 - cos120 ) = 1/8( 1 + 1/2 ) = 3/16

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3 years ago

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2 years ago

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3 years ago