化简cos20—cos30

我做来的答案是这样的.

cos20-cos10
=(1-2sin^210)-cos20cos10+si20sin10
提公因式,把cos10提出来

然后并同类项.

结果是:

2*sin10*sin10*cos10

because

cosA+cosB=2cos((A+B)/2)sin((A-B)/2)

so

cos20-cos30
= cos(20)+cos(150)
= 2cos(85)sin(-65)
=-2cos(85)sin(65)

--------or--------

because cosx=sin(90 degree-x)

so cos20-cos30 = sin70-sin60

三角函数的和差化积 和 积化和差