计算下列几个式子，①tan25°+tan35°+3tan25°tan35°，②1+tan15°1?tan15°，③2（sin35°cos25°+sin计算下列几个式子，①tan25°+tan35°+3tan25°tan35°，②1+tan15°1?tan15°，③2（sin35°cos25°+sin55°cos65°）．结果

Question

计算下列几个式子，①tan25°+tan35°+3tan25°tan35°，②1+tan15°1?tan15°，③2（sin35°cos25°+sin
计算下列几个式子，①tan25°+tan35°+√(3)tan25°tan35°，②(1+tan15°)/(1?tan15°)，③2（sin35°cos25°+sin55°cos65°）．结果为√(3)的是（　　）
A．①②
B．①③
C．①②③
D．②③

√(3)tan25°tan35°，②(1+tan15°)/(1?tan15°)，③2（sin35°cos25°+sin55°cos65°）．结果为√(3)的是（　　）
A．①②
B．①③
C．①②③
D．②③
√(3)

3

3(1+tan15°)/(1?tan15°)，③2（sin35°cos25°+sin55°cos65°）．结果为√(3)的是（　　）
A．①②
B．①③
C．①②③
D．②③
(1+tan15°)/(1?tan15°)1+tan15°1+tan15°1?tan15°1?tan15°√(3)的是（　　）
A．①②
B．①③
C．①②③
D．②③
√(3)

3

3

Answer 1

①tan25°+tan35°+√(3)tan25°tan35°=tan（25°+35°）（1-tan25°tan35°）+√(3)tan25°tan35°
=√(3)（1-tan25°tan35°）+√(3)tan25°tan35°=√(3)．
②(1+tan15°)/(1?tan15°)=(1+(sin15°)/(cos15°))/(1?(sin15°)/(cos15°))=(cos15°+sin15°)/(cos15°?sin15°)=(√(2)sin(45°+15°))/(√(2)sin(45°?30°))=(sin60°)/(sin30°)=√(3)
③2（sin35°cos25°+sin55°cos65°）=2（sin35°cos25°+cos35°sin25°）=2sin60°=√(3)
故选：C． √(3)

3

33tan25°tan35°=tan（25°+35°）（1-tan25°tan35°）+√(3)tan25°tan35°
=√(3)（1-tan25°tan35°）+√(3)tan25°tan35°=√(3)．
②(1+tan15°)/(1?tan15°)=(1+(sin15°)/(cos15°))/(1?(sin15°)/(cos15°))=(cos15°+sin15°)/(cos15°?sin15°)=(√(2)sin(45°+15°))/(√(2)sin(45°?30°))=(sin60°)/(sin30°)=√(3)
③2（sin35°cos25°+sin55°cos65°）=2（sin35°cos25°+cos35°sin25°）=2sin60°=√(3)
故选：C． √(3)

3

33tan25°tan35°
=√(3)（1-tan25°tan35°）+√(3)tan25°tan35°=√(3)．
②(1+tan15°)/(1?tan15°)=(1+(sin15°)/(cos15°))/(1?(sin15°)/(cos15°))=(cos15°+sin15°)/(cos15°?sin15°)=(√(2)sin(45°+15°))/(√(2)sin(45°?30°))=(sin60°)/(sin30°)=√(3)
③2（sin35°cos25°+sin55°cos65°）=2（sin35°cos25°+cos35°sin25°）=2sin60°=√(3)
故选：C． √(3)

3

33（1-tan25°tan35°）+√(3)tan25°tan35°=√(3)．
②(1+tan15°)/(1?tan15°)=(1+(sin15°)/(cos15°))/(1?(sin15°)/(cos15°))=(cos15°+sin15°)/(cos15°?sin15°)=(√(2)sin(45°+15°))/(√(2)sin(45°?30°))=(sin60°)/(sin30°)=√(3)
③2（sin35°cos25°+sin55°cos65°）=2（sin35°cos25°+cos35°sin25°）=2sin60°=√(3)
故选：C． √(3)

3

33tan25°tan35°=√(3)．
②(1+tan15°)/(1?tan15°)=(1+(sin15°)/(cos15°))/(1?(sin15°)/(cos15°))=(cos15°+sin15°)/(cos15°?sin15°)=(√(2)sin(45°+15°))/(√(2)sin(45°?30°))=(sin60°)/(sin30°)=√(3)
③2（sin35°cos25°+sin55°cos65°）=2（sin35°cos25°+cos35°sin25°）=2sin60°=√(3)
故选：C． √(3)

3

33．
②(1+tan15°)/(1?tan15°)=(1+(sin15°)/(cos15°))/(1?(sin15°)/(cos15°))=(cos15°+sin15°)/(cos15°?sin15°)=(√(2)sin(45°+15°))/(√(2)sin(45°?30°))=(sin60°)/(sin30°)=√(3)
③2（sin35°cos25°+sin55°cos65°）=2（sin35°cos25°+cos35°sin25°）=2sin60°=√(3)
故选：C． (1+tan15°)/(1?tan15°)1+tan15°1+tan15°1+tan15°1?tan15°1?tan15°1?tan15°=(1+(sin15°)/(cos15°))/(1?(sin15°)/(cos15°))=(cos15°+sin15°)/(cos15°?sin15°)=(√(2)sin(45°+15°))/(√(2)sin(45°?30°))=(sin60°)/(sin30°)=√(3)
③2（sin35°cos25°+sin55°cos65°）=2（sin35°cos25°+cos35°sin25°）=2sin60°=√(3)
故选：C． (1+(sin15°)/(cos15°))/(1?(sin15°)/(cos15°))1+(sin15°)/(cos15°)1+(sin15°)/(cos15°)1+(sin15°)/(cos15°)sin15°sin15°sin15°cos15°cos15°cos15°1?(sin15°)/(cos15°)1?(sin15°)/(cos15°)1?(sin15°)/(cos15°)sin15°sin15°sin15°cos15°cos15°cos15°=(cos15°+sin15°)/(cos15°?sin15°)=(√(2)sin(45°+15°))/(√(2)sin(45°?30°))=(sin60°)/(sin30°)=√(3)
③2（sin35°cos25°+sin55°cos65°）=2（sin35°cos25°+cos35°sin25°）=2sin60°=√(3)
故选：C． (cos15°+sin15°)/(cos15°?sin15°)cos15°+sin15°cos15°+sin15°cos15°+sin15°cos15°?sin15°cos15°?sin15°cos15°?sin15°=(√(2)sin(45°+15°))/(√(2)sin(45°?30°))=(sin60°)/(sin30°)=√(3)
③2（sin35°cos25°+sin55°cos65°）=2（sin35°cos25°+cos35°sin25°）=2sin60°=√(3)
故选：C． (√(2)sin(45°+15°))/(√(2)sin(45°?30°))√(2)sin(45°+15°)√(2)sin(45°+15°)√(2)

2

22sin(45°+15°)√(2)sin(45°?30°)√(2)sin(45°?30°)√(2)

2

22sin(45°?30°)=(sin60°)/(sin30°)=√(3)
③2（sin35°cos25°+sin55°cos65°）=2（sin35°cos25°+cos35°sin25°）=2sin60°=√(3)
故选：C． (sin60°)/(sin30°)sin60°sin60°sin60°sin30°sin30°sin30°=√(3)
③2（sin35°cos25°+sin55°cos65°）=2（sin35°cos25°+cos35°sin25°）=2sin60°=√(3)
故选：C． √(3)

3

33
③2（sin35°cos25°+sin55°cos65°）=2（sin35°cos25°+cos35°sin25°）=2sin60°=√(3)
故选：C． √(3)

3

33
故选：C．