Question

Solve, sin 2theta= cos 3theta​

Answer 1

Answer:

Ф = ( 2 n + 1 / 2 ) π / 5 or  ( 2 n - 1 / 2 ) π , n € I

Step-by-step explanation:

Given :

cos 3 Ф = sin 2 Ф

Rewrite as :

cos 3 Ф = cos ( π / 2 - 2 Ф )

On comparing we get :

3 Ф =  π / 2 - 2 Ф

3 Ф + 2 Ф  =  π / 2

5 Ф = π / 2

We know if :

cos Ф = cos α

= > Ф = 2 n π ± α , n € I

Taking positive sign :

Ф = ( 2 n + 1 / 2 ) π / 5

Now taking negative sign :

Ф = ( 2 n - 1 / 2 ) π

Therefore , Ф = ( 2 n + 1 / 2 ) π / 5 or  ( 2 n - 1 / 2 ) π .