Question

daca sin(a+b)=5/13 si sin(a-b)=3/5. Sa se calculeze sina*sinb

Answer 1

$\sin a \sin b = \frac{1}{2} [\cos(a-b)-\cos(a+b)] \newline \cos(a-b) = \pm \sqrt{1-sin^2(a-b)} = \pm \frac{4}{5} \newline \cos(a+b) = \pm \sqrt{1-sin^2(a+b)} = \pm \frac{12}{13} \newline \sin a \sin b = \frac{1}{2} [ \pm \frac{4}{5} - (\pm \frac{12}{13} )]$
Acum depinde de interval, functia sin e pozitiva pe (0,π) si negativa pe (π,2π).