Sin x\3 cos П\5 - cos x\3 sin П\5 =√2\2

Question

Sin x\3 cos П\5 - cos x\3 sin П\5 =√2\2

Answer 1

Sinx/3cosπ/5-cosx/3sinπ/5=√/2
sin(x/3-π/5)=√2/2
x/3-π/5=(-1)ⁿπ/4+πn
x/3=(-1)ⁿπ/4+π/5+πn
x=(-1)3ⁿπ/4+3π/5+5πn