Question

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Answer 1

$\frac{Sin77^{0}+Sin43^{0}}{\sqrt{3}Cos13^{0}-Cos103^{0}}=\frac{2Sin\frac{77^{0}+43^{0}}{2}*Cos\frac{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}$