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Prove that: sin 47^0+cos 77^0=cos 17^0...

Prove that: `sin 47^0+cos 77^0=cos 17^0`

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We have to proof,
`sin(47^o)+cos(77^o)=cos(17^o)`
Let,
L.H.S.=`sin(47^o)+cos(77^o)`
L.H.S=`sin(47^o)+cos((90^o)-(13^o))`
L.H.S=`sin(47^o)+sin(13^o)`
As we know the formula,
`sin(A^o)+sin(B^o)= 2[sin(((A^o) +(B^o))/2)cos(((A^o)-(B^o))/2)]`
then, L.H.S=`sin(47^o)+sin(13^o)`
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