(1)(cosx)^2((tanx)^2+1)=1
所以(cosx)^2=16/17
所以(sinx)^2+sin2x+cos2x
=(sinx)^2+2sinxcosx+(cosx)^2-(sinx)^2
=(cosx)^2(2tanx+1)
=16/17*(-1/2+1)
=8/17
(2)an-a(n-1)=3*2^(2n-3)=(3/2)*4^(n-1)
a(n-1)-a(n-2)=(3/2)*4^(n-2)
.
a2-a1=3/2*4
所以an=a1+(a2-a1)+...+(an-a(n-1))
=2+3/2(4+4^2+...+4^(n-1))
=2+(3/2)*4(1-4^(n-1))/(1-4)
=4-2*4^(n-1)