Question

упростите:

 

sin^2(a)+sin^2(b)+2*sin(a)*sin(b)*cos(a+b)

Answer 1

sin^2(a)+sin^2(b)+2*sin(a)*sin(b)*cos(a+b)=

$=sin^2a+sin^2b+[cos(a-b)-cos(a+b)](cos(a+b)=$

$=sin^2a+sin^2b-cos^2(a+b)+cos(a-b)cos(a+b)=$

$=sin^2a+sin^2b-cos^2(a+b)+0,5(cos2a+cos2b)=$

$=sin^2a+sin^2b-cos^2(a+b)+0,5[(1-2sin^2a)+(1-2sin^2b)]=$

$1-cos^2(a+b)= sin^2(a+b)$

Ответ:  $sin^2(a+b).$