Question

Period of the function 2 sin⁴x + 3 cos⁴x is

Answer 1

Period of the given relation will be same as the sum of sin^4x and cos^4x
ie,

y=sin^4x+cos^4x

sin2x+cos2x)2−2sin2xcos2x=1−12sin22xy=sin4⁡x+cos4⁡x=(sin2⁡x+cos2⁡x)2−2sin2⁡xcos2⁡x=1−1/2sin^2 ⁡2x

We know that the period of sinx 2π. So, the period of sin⁡(2x) is π.

Hence, it is clear that the period of sin^2(2x)i π/2.

So, the period of the given function will be π/2.