1.tan2b=tan[(a+b)-(a-b)]
=[tan(a+b)-tan(a-b)]/[1+tan(a+b)tan(a-b)]
=(1/2-2)/[1+(1/2)*2]
=-3/4
2.cosA=√10/10,cosB=√5/5
--->sinA=3√10/10,sinB=2√5/5.
所以cosC=-cos(A+B)
=-(cosAcosB-sinAsinB)
=-√10/10*√5/5+3√10/10*2√5/5
=√2/2.
3.cosA=12/13,sinB=3/5
--->sinA=5/13,cosB=+'-4/5
cosC=-cos(A+B)
=-（cosAcosB-sinAsinB)
=33/65或63/65
4.pi/2<2<pi--->sin2>0,cos2<0
√(1-sin4)=√[(sin2)^2+(cos2)^2-2sin2cos2]=|sin2-cos2|
=sin2-cos2.
5.cos2t=sin(pi/2-2t)=sin[2(pi/4-t)]
=2tan(pi/4-t)/{1+[tan(pi/4-t)]^2}
=2(-0.5)/[1+(-0.5)^2]
=-4/5.
6.x^2-(sint+i)x-2-i=0有实数根
--->(x^2-xsint-2)-i(x+1)=0由复数相等的条件
--->x+1=0,x^2-xsint-2=0
--->x=-1,sint=(x^2-2)/x=(1-2)/(-1)=1
pi/2=<t=<3pi/2,sint=1--->cost=0
cos(t+pi/6)=costcos(pi/6)-sintsin(pi/6)
=1/2
