化简:sin7°+cos15°sin8°cos7°−sin15°sin8°的值为（）A.2+3B.2-3C.1+3D.3-1

Question

(sin7°+cos15°sin8°)/(cos7°−sin15°sin8°)的值为（　　）
A. 2+√(3)
B. 2-√(3)
C. 1+√(3)
D. √(3)-1(sin7°+cos15°sin8°)/(cos7°−sin15°sin8°)sin7°+cos15°sin8°sin7°+cos15°sin8°cos7°−sin15°sin8°cos7°−sin15°sin8°
√(3)
B. 2-√(3)
C. 1+√(3)
D. √(3)-1√(3)

3

3
√(3)
C. 1+√(3)
D. √(3)-1√(3)

3

3
√(3)
D. √(3)-1√(3)

3

3
√(3)-1√(3)

3

3

Answer 1

(sin7°+cos15°sin8°)/(cos7°−sin15°sin8°)
=(sin(15°−8°)+cos15°sin8°)/(cos(15°−8°)−sin15°sin8°)
=(sin15°cos8°)/(cos15°cos8°)
=(2sin15°cos15°)/(2cos15°cos15°)
=((1)/(2))/(1+cos30°)
=(1)/(2+√(3))
=2-√(3)．
故选B． (sin7°+cos15°sin8°)/(cos7°−sin15°sin8°)sin7°+cos15°sin8°sin7°+cos15°sin8°sin7°+cos15°sin8°cos7°−sin15°sin8°cos7°−sin15°sin8°cos7°−sin15°sin8°
=(sin(15°−8°)+cos15°sin8°)/(cos(15°−8°)−sin15°sin8°)
=(sin15°cos8°)/(cos15°cos8°)
=(2sin15°cos15°)/(2cos15°cos15°)
=((1)/(2))/(1+cos30°)
=(1)/(2+√(3))
=2-√(3)．
故选B． (sin(15°−8°)+cos15°sin8°)/(cos(15°−8°)−sin15°sin8°)sin(15°−8°)+cos15°sin8°sin(15°−8°)+cos15°sin8°sin(15°−8°)+cos15°sin8°cos(15°−8°)−sin15°sin8°cos(15°−8°)−sin15°sin8°cos(15°−8°)−sin15°sin8°
=(sin15°cos8°)/(cos15°cos8°)
=(2sin15°cos15°)/(2cos15°cos15°)
=((1)/(2))/(1+cos30°)
=(1)/(2+√(3))
=2-√(3)．
故选B． (sin15°cos8°)/(cos15°cos8°)sin15°cos8°sin15°cos8°sin15°cos8°cos15°cos8°cos15°cos8°cos15°cos8°
=(2sin15°cos15°)/(2cos15°cos15°)
=((1)/(2))/(1+cos30°)
=(1)/(2+√(3))
=2-√(3)．
故选B． (2sin15°cos15°)/(2cos15°cos15°)2sin15°cos15°2sin15°cos15°2sin15°cos15°2cos15°cos15°2cos15°cos15°2cos15°cos15°
=((1)/(2))/(1+cos30°)
=(1)/(2+√(3))
=2-√(3)．
故选B． ((1)/(2))/(1+cos30°)(1)/(2)(1)/(2)(1)/(2)1112221+cos30°1+cos30°1+cos30°
=(1)/(2+√(3))
=2-√(3)．
故选B． (1)/(2+√(3))1112+√(3)2+√(3)2+√(3)

3

33
=2-√(3)．
故选B． √(3)

3

33．
故选B．