Question

sin x * cos x , якщо sin x + cos x=1/2

Answer 1

Ответ:

$sinx+cosx=\dfrac{1}{2}\\\\\\(sinx+cosx)^2=\dfrac{1}{4}\\\\\\\underbrace {sin^2x+cos^2x}_{1}+2\, sinx\cdot cosx=\dfrac{1}{4}\\\\\\1+2\, sinx\cdot cosx=\dfrac{1}{4}\\\\\\2\, sinx\cdot cosx=-\dfrac{3}{4}\\\\\\sinx\cdot cosx=-\dfrac{3}{8}$