Question

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Answer 1

$frac{Sin77^{0}+Sin43^{0}}{sqrt{3}Cos13^{0}-Cos103^{0}}=frac{2Sinfrac{77^{0}+43^{0}}{2}*Cosfrac{77^{0}-43^{0}}{2}}{sqrt{3}Cos13^{0}-Cos(90^{0}+13^{0})}=frac{2Sin60^{0}*Cos17^{0}}{sqrt{3}Cos13^{0}+Sin13^{0}}=frac{2*frac{sqrt{3} }{2}*Cos17^{0}}{2(frac{sqrt{3}}{2}Cos13^{0}+frac{1}{2}Sin13^{0})}=$$frac{sqrt{3}*Cos17^{0}}{2(Cos30^{0}*Cos13^{0}+Sin30^{0}*Sin13^{0})}=frac{sqrt{3}*Cos17^{0}}{2*Cos(30^{0}-13^{0})}=frac{sqrt{3}*Cos17^{0}}{2*Cos17^{0} }=frac{sqrt{3}}{2}$