Question

Упростите:
cosa-cos2a​

Answer 1

cosα-cos2α=cosα-cos²α+sin²α=cosα-1+2sin²α=cosα-cos²α+1-cos²α=

cosα-2cos²α+1=(2сosα+1)*(1-cosα)

cosα-1+2sin²α=2sin²α-2sin²α/2=8sin²α/2*cos²α/2-2sin²α/2=

2sin²α/2*(4cos²α/2-1)=2sin²α/2*(2cosα/2-1)(2cosα/2+1)