Bài tập: 1. CMR: $cos(a+b).cos(a-b)=cos^2a-sin^2a$ 2. CMR: $\frac{1-cosx+cos2x}{sin2x-sinx}=cotx$

1.

`cos(a+b).cos(a-b)`

`=(cosa.cosb-sina.sinb).(cosa.cosb+sina.sinb)`

`=cos^2a.cos^2b-sin^2a.sin^2b`

`=cos^2b.(1-sin^2a)-sin^2a.(1-cos^2b)`

`=cos^2b-cos^2b.sin^2a-sin^2a+cos^2b.sin^2a`

`=cos^2b-sin^2a` (đpcm)

2.

`\frac{1-cosx+cos2x}{sin2x-sinx}`

`=\frac{1-cosx+2cos^2x-1}{2.sinx.cosx-sinx}`

`=\frac{cosx(2cosx-1)}{sinx(2cosx-1)}`

`=\frac{cosx}{sinx}=cotx` (đpcm)