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Question Number 27104 by ktomboy1992 last updated on 02/Jan/18

sin45^(o ) cos45^o +(√(3   sin 60°=?))

$$\mathrm{sin45}^{{o}\:} \mathrm{cos45}^{{o}} +\sqrt{\mathrm{3}\:\:\:\mathrm{sin}\:\mathrm{60}°=?} \\ $$

Commented by mrW1 last updated on 02/Jan/18

what do you mean?  sin45^(o ) cos45^o +(√3) sin 60° or  sin45^(o ) cos45^o +(√(3 sin 60°)) ?    sin45^(o ) cos45^o +(√3) sin 60° = (1/(√2))×(1/(√2))+(√3)×((√3)/2)=(1/2)+(3/2)=(4/2)=2  sin45^(o ) cos45^o +(√(3 sin 60°)) = (1/(√2))×(1/(√2))+(√(3×((√3)/2)))=(1/2)+((√(6(√3)))/2)=((1+(√(6(√3))))/2)

$${what}\:{do}\:{you}\:{mean}? \\ $$$$\mathrm{sin45}^{{o}\:} \mathrm{cos45}^{{o}} +\sqrt{\mathrm{3}}\:\mathrm{sin}\:\mathrm{60}°\:{or} \\ $$$$\mathrm{sin45}^{{o}\:} \mathrm{cos45}^{{o}} +\sqrt{\mathrm{3}\:\mathrm{sin}\:\mathrm{60}°}\:? \\ $$$$ \\ $$$$\mathrm{sin45}^{{o}\:} \mathrm{cos45}^{{o}} +\sqrt{\mathrm{3}}\:\mathrm{sin}\:\mathrm{60}°\:=\:\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}×\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}+\sqrt{\mathrm{3}}×\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{3}}{\mathrm{2}}=\frac{\mathrm{4}}{\mathrm{2}}=\mathrm{2} \\ $$$$\mathrm{sin45}^{{o}\:} \mathrm{cos45}^{{o}} +\sqrt{\mathrm{3}\:\mathrm{sin}\:\mathrm{60}°}\:=\:\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}×\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}+\sqrt{\mathrm{3}×\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}=\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{6}\sqrt{\mathrm{3}}}}{\mathrm{2}}=\frac{\mathrm{1}+\sqrt{\mathrm{6}\sqrt{\mathrm{3}}}}{\mathrm{2}} \\ $$

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