Question

Find all solutions in radians using exact values only. Sin3xCos2x+Cos3xSin2x=1

Answer 1

\[\sin 3x \cos 2x+\cos 3x \sin 2x=1\]
\[\sin 5x=1=\sin \frac{ \pi }{ 2 }=\sin \left( 2n \pi+\frac{ \pi }{ 2 } \right),where n=0,1,2,3,....\]
\[5x=2n \pi+\frac{ \pi }{ 2 }, where n is an integer.\]
\[x=\frac{ 2n \pi }{ 5 }+\frac{ \pi }{ 10},where n is an integer.\]