Question

Find the general solution of
sec2 2x = 1 -tan 2x​

Answer 1

Answer:

x = n π / 2  OR   x = n π / 2+ 3 π / 8

Step-by-step explanation:

Given :

sec² 2 x = 1 - tan 2 x

We know :

sec² x = 1 + tan² x

= > 1 + tan² 2 x = 1 - tan 2 x

= > tan² 2 x + tan 2 x = 0

Take out tan 2 x common :

= > tan 2 x ( tan 2 x + 1 ) = 0

Case first :

tan 2 x = 0

= > 2 x = n π

= > x = n π / 2

Case second :

( tan 2 x + 1 ) = 0

tan 2 x = - 1

= > tan 2 x = tan ( π - π / 4 )

= > tan 2 x = tan ( 3 π / 4 )

We know if :

tan Ф = tan α

= > Ф = n π + α

= > 2 x = n π + 3 π / 4

= > x = n π / 2+ 3 π / 8

Therefore , we get general solution of given equation.