Question

Find the general solutions of the equation ( 1 - tan theta ) ( 1 + sin 2 theta ) = 1 + tan theta pls answer this and pls dont link to any other question

Answer 1

(1 - tan x) (1 + sin 2x) = 1 + tan x

1+ sin 2x = 1 + (2 tan x)(1+ tan² x)  = (1+ tan x)²/(1 + tan² x)

so either 1 + tan x = 0
            =>  tan x = -1    =>  x = -π/4 + n π,  n= integer.

or, (1 - tan x)(1+ tan x) = 1 + tan² x
            =>  tan² x = 0      =>   x = n π,  n = integer.     

Answer 2

Answer:

Step-by-step explanation:

(1 - tan x) (1 + sin 2x) = 1 + tan x

1+ sin 2x = 1 + (2 tan x)(1+ tan² x)  = (1+ tan x)²/(1 + tan² x)

so either 1 + tan x = 0

           =>  tan x = -1    =>  x = -π/4 + n π,  n= integer.

or, (1 - tan x)(1+ tan x) = 1 + tan² x

           =>  tan² x = 0      =>   x = n π,  n = integer.