Question

Rewrite
as a sum or
difference.
10sin50cos30

Answer 1

we know that :

$\displaystyle \sf sin(P)+sin(Q) =2\cdot sen\left(\frac{P+Q}{2}\right)\cdot cos\left(\frac{P-Q}{2}\right)$

so :

$\displaystyle \sf 2\cdot sin(50)\cdot cos(30) = sin(P)+sin(Q)\\\\\\ 10\cdot sin(50)\cdot cos(30) = 5\cdot [sin(P)+sin(Q)] \\\\\\ \left \begin{array}{I}\displaystyle \sf \frac{P+Q}{2} = 50 \to P+Q = 100 \\\\\\ \displaystyle \sf \frac{P-Q }{2} = 30 \to P-Q = 60 \end{array } \right\} \to 2P = 160 \to P = 80 \ , \ Q = 20\\\\\\\\ \boxed{\sf 10\cdot sin(50)\cdot cos(30) = 5\cdot \left[\ sin(80)+sin(20)\ \right] }\checkmark$