Question

Find the general solution for the equation

Sec 2 2x = 1 – Tan 2x

Answer 1

Given:

Equation =  Sec²2x = 1 – Tan 2x

To find:

General Solution

Solution:

Sec² 2x=1−tan2x

1+t²an 2x=1−tan2x

tan² 2x+tan2x=0

tan2x(tan2x+1)=0

tan2x =0 or tan 2x+1=0

Now, tan2x = 0

tan2x = tan0

2x = nπ + 0,n ∈Z

x = nπ/2 , n∈Z

tan 2x +1 = 0

tan 2x = -1 = - tanπ/4

= tan ( π - π/4)

= tan 3π/4

2x = n

Sec 2 2x = 1 – Tan 2x  

2x = nπ + 3π/4,

x = nπ/2 + 3π/8

Answer: Therefore the general solution is nπ/2 or nπ/2 + 3π/8

Answer 2

Answer:

Here is the answer.

Step-by-step explanation:

Observe the quadant, otherwise ur answer will be wrong