Question

已知向量a=(sinx,3/4),b=(cosx,-1).当a‖b时求cos^2x-sin^2x的值

Answer 1

由a//b得sinx=-3/4cosx,再由(cosx)*2+(sinx)*2=1得(cosx)*2=16/25
(cosx)^2-sin(2x)=cosx(cosx-2sinx)=cosx(cosx+3/2cosx)=5/2(cosx)*2=8/5

Answer 2

a//b
=> sinx/(3/4) = cosx/(-1)
-4sinx=3cosx
tanx = -3/4
(cosx)^2 = (4/5)^2 = 16/25

(cosx)^2 - (sinx)^2
= 2(cosx)^2-1
=2(16/25)-1
=7/25