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Trignometry

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 Joined: 9 Jul 2012 Post: 2
9 Jul 2012 11:51:19 IST
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nice and hard
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Trigonometry

16sin(20)sin(40)sin(60)sin(80)=3

New kid on the Block

Joined: 15 May 2012
Posts: 6
9 Jul 2012 16:40:44 IST
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it can be easily proved that: sinx * sin(60+x)* sin (60-x)=sin(3x)/4so in this case take 16sin60 aside and apply the above taking x=20...to get..16sin(60)*sin(60)/4=4sin^2(60)=3

New kid on the Block

Joined: 9 Jul 2012
Posts: 2
9 Jul 2012 18:10:02 IST
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16sin(20)sin(40)sin(60)sin(80)=3

then

sin(20)sin(40)sin(60)sin(80)=3/16

√3/2{ sin(20)sin(40) sin(80)}

√3/2{ sin(20[1/2(cos(40) – cos(120))}

√3/4{ sin(20)cos(40) – sin(20) cos(120))}

√3/4{(1/2{sin(60)-sin(20)) –sin(20)*(-1/2)}        { cos 120=-1/2}

√3/8{√3/2- sin(20)+ sin(20)}

√3/8{{√3/2+0}

3/16

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