165度的正弦、余弦、正切值

解：
2sin²15°=1-cos30°
sin15°=√[(1-cos30°)/2]
=√[(1- √3/2)/2]
=√[(2-√3)/4]
=√[4-2√3)/8]
=√[(√3-1)²/(2√2)²]
=(√3-1)/(2√2)
=(√6-√2)/4
cos15°=√(1-sin²15°)=(√6+√2)/4
sin165°=sin(180°-15°)=sin15°=(√6-√2)/4
cos165°=-cos(180°-15°)=-cos15°=-(√6+√2)/4
tan165°=sin165°/cos165°=[(√6-√2)/4]/[-(√6+√2)/4]
=-(√6-√2)/(√6+√2)
=-(√6-√2)²/4
=√3-2
tan165°的正弦值为(√6-√2)/4，余弦值为-(√6+√2)/4，正切值为√3-2

sin165°
=sin15°
=sin(45°-30°)
=(√6-√2)/4
cos165°
=cos(180°-15°)
=-cos15°
=-(√6+√2)/4
tan165°=sin165°/cos165°=[(√6-√2)/4]/[-(√6+√2)/4]
=-(√6-√2)/(√6+√2)
=-(√6-√2)²/4
=√3-2