Question

Find the periods of the following functions. X
i) 2sin⁴x+cos⁴x​

Answer 1

Answer:

Correct option is

A

π/2

We have,

(x)=sin

4

x+cos

4

x

⇒(x)=(sin

2

x)+(cos

2

x)

2

2sin

2

xcos

2

x

⇒(x)=(sin

2

x+cos

2

x)

2

−

2

1

(2sinxcosx)

2

⇒(x)=1−

2

1

{sin

2

2x}

⇒(x)=1−

2

1

{

2

1−cos4x

}

⇒(x)=

4

3

−

4

1

cos4x.

Since cos4x is a periodic function with period

4

2π

=

2

π

So, (x) is periodic with period

2

π

.