We have, cos22x+sin‌23x=1 ‌⇒‌‌1−sin‌22x+sin‌33x=1 ‌⇒‌‌sin‌23x=sin‌22x⇒3x=nx±2x On taking + ve sign, we get x=nπ,n∈Z On taking - ve sign, we get ‌3x=nπ−2x,n∈Z ‌5x=nπ,n∈Z ‌x=‌
nπ
5
,n∈Z ‌x∈{‌
nπ
5
‌rvert‌n∈Z} ∴‌‌x∈{‌
nπ
5
‌rvert‌n∈Z}∪{nπ∣n∈Z} ‌={‌
nπ
5
‌rvert‌n∈Z} Hence, solution set is {x∕x=‌