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Prove that: sin 40^0+sin 20^0=cos10^0...

Prove that: `sin 40^0+sin 20^0=cos10^0`

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To proof: `sin(40^o)+sin(20^o)=cos(10^o)`
Let,
L.H.S=`sin(40^o)+sin(20^o)`
As we know the formula,
`sinA+sinB=2sin((A+B)/2)(cos((A-B)/2)`
So, L.H.S`=2sin(((40^o)+(20^o))/2).cos(((40^o)-(20^o))/2)`
L.H.S=` 2sin30^o cos10^o`
L.H.S=`(2*1/2)cos(10^o)`
...
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